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Volumn 115, Issue 2-3, 1998, Pages 460-488

Nonclassical reductions of a 3+1-cubic nonlinear Schrödinger system

Author keywords

Algorithms; Differential Gr bner bases; Involutivity; Nonlinear Schr dinger system; Symmetry analysis; Symmetry reduction

Indexed keywords

ALGEBRA; ALGORITHMS; NONLINEAR OPTICS; VECTORS;

EID: 0032477225     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0010-4655(98)00136-2     Document Type: Article
Times cited : (29)

References (86)
  • 2
    • 0002004721 scopus 로고
    • Solitons, Nonlinear Evolution Equations and Inverse Scattering L.M.S.
    • Cambridge Univ. Press, Cambridge
    • M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering L.M.S. Lect. Notes Math., Vol. 149 (Cambridge Univ. Press, Cambridge, 1991).
    • (1991) Lect. Notes Math. , vol.149
    • Ablowitz, M.J.1    Clarkson, P.A.2
  • 3
    • 84975607685 scopus 로고
    • Overview of transverse effects in nonlinear-optical systems
    • N.B. Abraham, W.J. Firth, Overview of transverse effects in nonlinear-optical systems, J. Opt. Soc. Am. B 7 (1990) 951-962.
    • (1990) J. Opt. Soc. Am. B , vol.7 , pp. 951-962
    • Abraham, N.B.1    Firth, W.J.2
  • 5
    • 0003332531 scopus 로고    scopus 로고
    • Scaling, Self-similarity, and Intermediate Asymptotics
    • Cambridge Univ. Press, Cambridge
    • G.I. Barenblatt, Scaling, Self-similarity, and Intermediate Asymptotics, Cambridge Texts in Applied Mathematics, Vol. 14 (Cambridge Univ. Press, Cambridge, 1996).
    • (1996) Cambridge Texts in Applied Mathematics , vol.14
    • Barenblatt, G.I.1
  • 6
    • 0242323668 scopus 로고
    • Singular point analysis and integrals of motion for coupled nonlinear Schrödinger equations
    • G. Baumann, W.G. Glöcke, T.F. Nonnenmacher, Singular point analysis and integrals of motion for coupled nonlinear Schrödinger equations, Proc. R. Soc. London A 434 (1991) 263-278.
    • (1991) Proc. R. Soc. London A , vol.434 , pp. 263-278
    • Baumann, G.1    Glöcke, W.G.2    Nonnenmacher, T.F.3
  • 8
    • 0023150231 scopus 로고
    • Polarization instabilities for solitons in birefringent fibers
    • K.J. Blow, N.J. Doran, D. Wood, Polarization instabilities for solitons in birefringent fibers, Opt. Lett. 12 (1987) 202-204.
    • (1987) Opt. Lett. , vol.12 , pp. 202-204
    • Blow, K.J.1    Doran, N.J.2    Wood, D.3
  • 9
    • 0000478462 scopus 로고
    • The general similarity solution of the heat equation
    • G.W. Bluman, J.D. Cole, The general similarity solution of the heat equation, J. Math. Mech. 18 (1969) 1025-1042.
    • (1969) J. Math. Mech. , vol.18 , pp. 1025-1042
    • Bluman, G.W.1    Cole, J.D.2
  • 10
    • 0003339099 scopus 로고
    • Symmetries and Differential Equations
    • Springer, New York
    • G.W. Bluman, S. Kumei, Symmetries and Differential Equations, Appl. Math. Sci., Vol. 81 (Springer, New York, 1989).
    • (1989) Appl. Math. Sci. , vol.81
    • Bluman, G.W.1    Kumei, S.2
  • 11
    • 0000133634 scopus 로고
    • Representation for the radical of a finitely generated differential ideal
    • Montreal, A. Levelt, ed. (ACM Press, New York)
    • F. Boulier, D. Lazard, F. Ollivier, M. Petitot, Representation for the radical of a finitely generated differential ideal, in: Proc. ISSAC '95, Montreal, 1995, A. Levelt, ed. (ACM Press, New York).
    • (1995) Proc. ISSAC '95
    • Boulier, F.1    Lazard, D.2    Ollivier, F.3    Petitot, M.4
  • 13
    • 85034654309 scopus 로고
    • Applications of Gröbner bases in non-linear computational geometry
    • Mathematical Aspects of Scientific Software, J.R. Rice, ed. Springer, New York
    • B. Buchberger, Applications of Gröbner bases in non-linear computational geometry, in: Mathematical Aspects of Scientific Software, IMA Volumes in Mathematics and its Applications, Vol. 14, J.R. Rice, ed. (Springer, New York, 1988) pp. 52-80.
    • (1988) IMA Volumes in Mathematics and Its Applications , vol.14 , pp. 52-80
    • Buchberger, B.1
  • 15
    • 85034782464 scopus 로고
    • Groebner bases and differential algebra
    • Proc. AAECC5, Menorca, Spain, L. Huguet, A. Poli, eds.
    • G. Carrà-Ferro, Groebner bases and differential algebra in: Proc. AAECC5, Menorca, Spain, Lect. Notes Comp. Sci., Vol. 356, L. Huguet, A. Poli, eds. (1989) 129-140.
    • (1989) Lect. Notes Comp. Sci. , vol.356 , pp. 129-140
    • Carrà-Ferro, G.1
  • 16
    • 0002203411 scopus 로고
    • On term-orderings and rankings
    • Computational Algebra, K.G. Fischer et al., eds. Marcel Dekker, New York
    • G. Carrà-Ferro, W.Y. Sit, On term-orderings and rankings, in: Computational Algebra, Lect. Notes Pure Appl. Math., Vol. 151, K.G. Fischer et al., eds. (Marcel Dekker, New York, 1993) pp. 31-77.
    • (1993) Lect. Notes Pure Appl. Math. , vol.151 , pp. 31-77
    • Carrà-Ferro, G.1    Sit, W.Y.2
  • 17
    • 0026222880 scopus 로고
    • The computer calculation of Lie point symmetries of large systems of differential equations
    • B. Champagne, W. Hereman, P. Winternitz, The computer calculation of Lie point symmetries of large systems of differential equations, Comput. Phys. Commun. 66 (1991) 319-340.
    • (1991) Comput. Phys. Commun. , vol.66 , pp. 319-340
    • Champagne, B.1    Hereman, W.2    Winternitz, P.3
  • 18
    • 0002551552 scopus 로고
    • Dimensional reductions and exact solutions of a generalized nonlinear Schrödinger equation
    • P.A. Clarkson, Dimensional reductions and exact solutions of a generalized nonlinear Schrödinger equation, Nonlinearity 5 (1992) 453-472.
    • (1992) Nonlinearity , vol.5 , pp. 453-472
    • Clarkson, P.A.1
  • 19
    • 33646984319 scopus 로고
    • Nonclassical symmetry reductions of the Boussinesq equation
    • P.A. Clarkson, Nonclassical symmetry reductions of the Boussinesq equation, Chaos, Solitons & Fractals 5 (1995) 2261-2301.
    • (1995) Chaos, Solitons & Fractals , vol.5 , pp. 2261-2301
    • Clarkson, P.A.1
  • 20
    • 18944400520 scopus 로고
    • New similarity solutions of the Boussinesq equation
    • P.A. Clarkson, M.D. Kruskal, New similarity solutions of the Boussinesq equation, J. Math. Phys. 30 (1989) 2201-2213.
    • (1989) J. Math. Phys. , vol.30 , pp. 2201-2213
    • Clarkson, P.A.1    Kruskal, M.D.2
  • 21
    • 0005144466 scopus 로고    scopus 로고
    • The classical, direct and nonclassical methods for symmetry reductions of nonlinear partial differential equations
    • P.A. Clarkson, D.K. Ludlow, T.J. Priestley, The classical, direct and nonclassical methods for symmetry reductions of nonlinear partial differential equations, Meth. Appl. Anal. 4 (1997) 173-195.
    • (1997) Meth. Appl. Anal. , vol.4 , pp. 173-195
    • Clarkson, P.A.1    Ludlow, D.K.2    Priestley, T.J.3
  • 22
    • 43949149919 scopus 로고
    • Symmetry reductions and exact solutions of a class of nonlinear heat equations
    • P.A. Clarkson, E.L. Mansfield, Symmetry reductions and exact solutions of a class of nonlinear heat equations, Physica D 70 (1993) 250-288.
    • (1993) Physica D , vol.70 , pp. 250-288
    • Clarkson, P.A.1    Mansfield, E.L.2
  • 23
    • 0028699959 scopus 로고
    • Algorithms for the nonclassical method of symmetry reduction
    • P.A. Clarkson, E.L. Mansfield, Algorithms for the nonclassical method of symmetry reduction, SIAM J. Appl. Math. 54 (1994) 1693-1719.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1693-1719
    • Clarkson, P.A.1    Mansfield, E.L.2
  • 26
    • 0347648368 scopus 로고    scopus 로고
    • Moving Coframes II
    • preprint, University of Minnesota, USA, to appear
    • M. Fels, P.J. Olver, Moving Coframes II, preprint, University of Minnesota, USA, in Acta Appl. Math., to appear.
    • Acta Appl. Math.
    • Fels, M.1    Olver, P.J.2
  • 27
    • 0001719798 scopus 로고
    • Conditional symmetry of the equations of Mathematical Physics
    • W.I. Fushchich, Conditional symmetry of the equations of Mathematical Physics, Ukrain. Math. J. 43 (1991) 1456-1470.
    • (1991) Ukrain. Math. J. , vol.43 , pp. 1456-1470
    • Fushchich, W.I.1
  • 28
    • 0005161089 scopus 로고
    • Exact solutions for optical wave propagations including transverse effects
    • L. Gagnon, Exact solutions for optical wave propagations including transverse effects, J. Opt. Soc. Am. B 7 (1990) 1098-1102.
    • (1990) J. Opt. Soc. Am. B , vol.7 , pp. 1098-1102
    • Gagnon, L.1
  • 29
    • 0003869248 scopus 로고
    • Self-similar solutions for a coupled system of nonlinear Schrödinger equations
    • L. Gagnon, Self-similar solutions for a coupled system of nonlinear Schrödinger equations, J. Phys. A 25 (1992) 2649-2667.
    • (1992) J. Phys. A , vol.25 , pp. 2649-2667
    • Gagnon, L.1
  • 30
    • 0040404110 scopus 로고
    • Lie symmetries of a generalised nonlinear Schrödinger equation: III. Reductions to third-order ordinary differential equations
    • L. Gagnon, B. Grammaticos, A. Ramani, P. Winternitz, Lie symmetries of a generalised nonlinear Schrödinger equation: III. Reductions to third-order ordinary differential equations, J. Phys. A 22 (1989) 499-509.
    • (1989) J. Phys. A , vol.22 , pp. 499-509
    • Gagnon, L.1    Grammaticos, B.2    Ramani, A.3    Winternitz, P.4
  • 31
    • 84975662145 scopus 로고
    • Nonlinear radiation modes connected to parabolic graded-index profiles by the lens transformation
    • L. Gagnon, C. Paré, Nonlinear radiation modes connected to parabolic graded-index profiles by the lens transformation, J. Opt. Soc. Am. B 8 (1990) 601-607.
    • (1990) J. Opt. Soc. Am. B , vol.8 , pp. 601-607
    • Gagnon, L.1    Paré, C.2
  • 32
    • 0009050620 scopus 로고
    • Lie symmetries of a generalised nonlinear Schrödinger equation: I. the symmetry group and its subgroups
    • L. Gagnon, P. Winternitz, Lie symmetries of a generalised nonlinear Schrödinger equation: I. The symmetry group and its subgroups, J. Phys. A 21 (1988) 1493-1511.
    • (1988) J. Phys. A , vol.21 , pp. 1493-1511
    • Gagnon, L.1    Winternitz, P.2
  • 33
    • 0042182371 scopus 로고
    • Lie symmetries of a generalised nonlinear Schrödinger equation: II. Exact solutions
    • L. Gagnon, P. Winternitz, Lie symmetries of a generalised nonlinear Schrödinger equation: II. Exact solutions, J. Phys. A 22 (1989) 469-497.
    • (1989) J. Phys. A , vol.22 , pp. 469-497
    • Gagnon, L.1    Winternitz, P.2
  • 34
    • 0007566683 scopus 로고
    • Exact solutions of the cubic and quintic nonlinear Schrödinger equation for a cylindrical geometry
    • L. Gagnon, P. Winternitz, Exact solutions of the cubic and quintic nonlinear Schrödinger equation for a cylindrical geometry, Phys. Rev. A 39 (1989) 296-306.
    • (1989) Phys. Rev. A , vol.39 , pp. 296-306
    • Gagnon, L.1    Winternitz, P.2
  • 35
    • 0002300466 scopus 로고
    • Exact solutions of the spherical quintic nonlinear Schrödinger equation
    • L. Gagnon, P. Winternitz, Exact solutions of the spherical quintic nonlinear Schrödinger equation, Phys. Lett. A 134 (1989) 276-281.
    • (1989) Phys. Lett. A , vol.134 , pp. 276-281
    • Gagnon, L.1    Winternitz, P.2
  • 36
    • 0039811565 scopus 로고
    • Non-Painlevé reductions of nonlinear Schrödinger equations
    • L. Gagnon, P. Winternitz, Non-Painlevé reductions of nonlinear Schrödinger equations, Phys. Rev. A 42 (1990) 5029-5030.
    • (1990) Phys. Rev. A , vol.42 , pp. 5029-5030
    • Gagnon, L.1    Winternitz, P.2
  • 39
    • 0027685141 scopus 로고
    • LIE: A PC program for Lie analysis of differential equations
    • A.K. Head, LIE: A PC program for Lie analysis of differential equations, Comput. Phys. Commun. 77 (1993) 241-248.
    • (1993) Comput. Phys. Commun. , vol.77 , pp. 241-248
    • Head, A.K.1
  • 40
    • 0002247504 scopus 로고
    • Review of symbolic software for the computation of Lie symmetries of differential equations
    • W. Hereman, Review of symbolic software for the computation of Lie symmetries of differential equations, Euromath Bull. 1 (1994) 45-79.
    • (1994) Euromath Bull. , vol.1 , pp. 45-79
    • Hereman, W.1
  • 41
    • 0347648360 scopus 로고
    • Research Report no. 77, Department of Mathematics, University of Canterbury, Christchurch, New Zealand
    • M. Hickman, The use of Maple in the search for symmetries, Research Report no. 77, Department of Mathematics, University of Canterbury, Christchurch, New Zealand (1993).
    • (1993) The use of Maple in the Search for Symmetries
    • Hickman, M.1
  • 45
    • 0000452782 scopus 로고
    • Soliton trapping and daughter waves in the Manakov model
    • D.J. Kaup, B.A. Malomed, Soliton trapping and daughter waves in the Manakov model, Phys. Rev. A 48 (1993) 599-604.
    • (1993) Phys. Rev. A , vol.48 , pp. 599-604
    • Kaup, D.J.1    Malomed, B.A.2
  • 46
    • 0001678923 scopus 로고
    • Nonclassical symmetry reduction: Example of the Boussinesq equation
    • D. Levi, P. Winternitz, Nonclassical symmetry reduction: example of the Boussinesq equation, J. Phys. A 22 (1989) 2915-2924.
    • (1989) J. Phys. A , vol.22 , pp. 2915-2924
    • Levi, D.1    Winternitz, P.2
  • 48
    • 0000763166 scopus 로고
    • On the theory of two-dimensional stationary self-focusing of electromagnetic waves
    • S.V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Sov. Phys. JETP 38 (1974) 248-253.
    • (1974) Sov. Phys. JETP , vol.38 , pp. 248-253
    • Manakov, S.V.1
  • 49
    • 21344484749 scopus 로고
    • Similarity reductions for variable-coefficient coupled nonlinear Schrödinger equations
    • N. Manganaro, D.F. Parker, Similarity reductions for variable-coefficient coupled nonlinear Schrödinger equations, J. Phys. A 26 (1993) 4093-4106.
    • (1993) J. Phys. A , vol.26 , pp. 4093-4106
    • Manganaro, N.1    Parker, D.F.2
  • 51
    • 0002016585 scopus 로고    scopus 로고
    • The differential algebra package diffgrob2
    • E.L. Mansfield, The differential algebra package diffgrob2, MapleTech 3 (1996) 33-37.
    • (1996) MapleTech , vol.3 , pp. 33-37
    • Mansfield, E.L.1
  • 52
    • 0345756484 scopus 로고    scopus 로고
    • preprint UKC/IMS/97/53, Institute of Mathematics and Statistics, University of Kent
    • E.L. Mansfield, Computer algebra for the Classification Problem, preprint UKC/IMS/97/53, Institute of Mathematics and Statistics, University of Kent (1997).
    • (1997) Computer Algebra for the Classification Problem
    • Mansfield, E.L.1
  • 53
    • 0031142055 scopus 로고    scopus 로고
    • Applications of the differential algebra package diffgrob2 to classical symmetries of differential equations
    • E.L. Mansfield, P.A. Clarkson, Applications of the differential algebra package diffgrob2 to classical symmetries of differential equations, J. Symb. Comput. 23 (1997) 517-533.
    • (1997) J. Symb. Comput. , vol.23 , pp. 517-533
    • Mansfield, E.L.1    Clarkson, P.A.2
  • 55
    • 0023293392 scopus 로고
    • Nonlinear pulse propagation in birefringent optical fibers
    • C.R. Menyuk, Nonlinear pulse propagation in birefringent optical fibers, IEEE J. Quantum Electron. QE-23 (1987) 174-176.
    • (1987) IEEE J. Quantum Electron. , vol.QE-23 , pp. 174-176
    • Menyuk, C.R.1
  • 56
    • 0024914687 scopus 로고
    • Pulse propagation in an elliptically birefringent Kerr medium
    • C.R. Menyuk, Pulse propagation in an elliptically birefringent Kerr medium, IEEE J. Quantum Electron. QE-25 (1989) 2674-2682.
    • (1989) IEEE J. Quantum Electron. , vol.QE-25 , pp. 2674-2682
    • Menyuk, C.R.1
  • 57
    • 0007071237 scopus 로고
    • Coupled nonlinear Schrödinger equations arising in monomode step-index optical fibre
    • G.K. Newboult, D.F. Parker, T.R. Faulker, Coupled nonlinear Schrödinger equations arising in monomode step-index optical fibre, J. Math. Phys. 30 (1989) 930-936.
    • (1989) J. Math. Phys. , vol.30 , pp. 930-936
    • Newboult, G.K.1    Parker, D.F.2    Faulker, T.R.3
  • 58
    • 0000923333 scopus 로고
    • Iterating the nonclassical symmetries method
    • M.C. Nucci, Iterating the nonclassical symmetries method, Physica D 78 (1994) 124-134.
    • (1994) Physica D , vol.78 , pp. 124-134
    • Nucci, M.C.1
  • 59
    • 0003317858 scopus 로고
    • Application of Lie groups to differential equations, 2nd ed
    • Springer, New York
    • P.J. Olver, Application of Lie groups to differential equations, 2nd ed., Graduate Texts in Mathematics, Vol. 107 (Springer, New York, 1993).
    • (1993) Graduate Texts in Mathematics , vol.107
    • Olver, P.J.1
  • 60
    • 0028768164 scopus 로고
    • Direct reduction and differential constraints
    • P.J. Olver, Direct reduction and differential constraints, Proc. Roy. Soc. London A 444 (1994) 509-523.
    • (1994) Proc. Roy. Soc. London A , vol.444 , pp. 509-523
    • Olver, P.J.1
  • 61
    • 0011002289 scopus 로고
    • Computations in differential and difference modules
    • E.V. Pankrat'ev, Computations in differential and difference modules, Acta Appl. Math. 16 (1989) 167-189.
    • (1989) Acta Appl. Math. , vol.16 , pp. 167-189
    • PankraT'Ev, E.V.1
  • 62
    • 0042317523 scopus 로고
    • Coupled cubic Schrödinger equations for axially symmetric waveguides
    • A. Donato, S. Giambo, eds. Cosenzam Editel
    • D.F. Parker, Coupled cubic Schrödinger equations for axially symmetric waveguides, in: Proc. Fourth Meeting on Waves and Stability in Continuous Media, A. Donato, S. Giambo, eds. (Cosenzam Editel, 1988) pp. 261-280.
    • (1988) Proc. Fourth Meeting on Waves and Stability in Continuous Media , pp. 261-280
    • Parker, D.F.1
  • 63
    • 0040918672 scopus 로고
    • Coupled nonlinear Schrödinger equations arising in fibre optics
    • D.F. Parker, G.K. Newboult, Coupled nonlinear Schrödinger equations arising in fibre optics, J. Phys. C 3 (1989) 137-146.
    • (1989) J. Phys. C , vol.3 , pp. 137-146
    • Parker, D.F.1    Newboult, G.K.2
  • 64
    • 36749111776 scopus 로고
    • Continuous subgroups of the fundamental groups of physics I. General method and the Poincaré group
    • J. Patera, P. Winternitz, H. Zassenhaus, Continuous subgroups of the fundamental groups of physics I. General method and the Poincaré group, J. Math. Phys. 16 (1975) 1597-1614.
    • (1975) J. Math. Phys. , vol.16 , pp. 1597-1614
    • Patera, J.1    Winternitz, P.2    Zassenhaus, H.3
  • 65
    • 21844490569 scopus 로고
    • Bright and dark soliton solutions to coupled nonlinear Schrödinger equations
    • R. Radhakrishnan, M. Lakshmanan, Bright and dark soliton solutions to coupled nonlinear Schrödinger equations, J. Phys. A 28 (1995) 2683-2692.
    • (1995) J. Phys. A , vol.28 , pp. 2683-2692
    • Radhakrishnan, R.1    Lakshmanan, M.2
  • 66
    • 0031212459 scopus 로고    scopus 로고
    • Inelastic collision and switching of coupled bright solitons in optical fibers
    • R. Radhakrishnan, M. Lakshmanan, J. Hietarinta, Inelastic collision and switching of coupled bright solitons in optical fibers, Phys. Rev. E 56 (1997) 2213-2216.
    • (1997) Phys. Rev. E , vol.56 , pp. 2213-2216
    • Radhakrishnan, R.1    Lakshmanan, M.2    Hietarinta, J.3
  • 67
    • 0000877015 scopus 로고
    • Integrability and singularity structure of coupled nonlinear Schrödinger equations
    • R. Radhakrishnan, R. Sahadevan, M. Lakshmanan, Integrability and singularity structure of coupled nonlinear Schrödinger equations. Chaos, Solitons & Fractals 5 (1995) 2315-2327.
    • (1995) Chaos, Solitons & Fractals , vol.5 , pp. 2315-2327
    • Radhakrishnan, R.1    Sahadevan, R.2    Lakshmanan, M.3
  • 68
    • 84972029082 scopus 로고
    • Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution
    • G.J. Reid, Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution, Euro. J. Appl. Math. 2 (1991) 293-318.
    • (1991) Euro. J. Appl. Math. , vol.2 , pp. 293-318
    • Reid, G.J.1
  • 69
    • 84971844577 scopus 로고
    • Finding abstract Lie symmetry algebras of differential equations without integrating determining equations
    • G.J. Reid, Finding abstract Lie symmetry algebras of differential equations without integrating determining equations, Euro. J. Appl. Math. 2 (1991) 319-340.
    • (1991) Euro. J. Appl. Math. , vol.2 , pp. 319-340
    • Reid, G.J.1
  • 70
    • 84992155013 scopus 로고
    • Algorithmic determination of commutation relations for Lie symmetry algebras of PDEs
    • California, P.S. Wang, ed. ACM Press, New York
    • G.J. Reid, I.G. Lisle, A. Boulton, A.D. Wittkopf, Algorithmic determination of commutation relations for Lie symmetry algebras of PDEs, in: Proc. ISSAC '92 Berkeley, California, P.S. Wang, ed. (ACM Press, New York, 1992) pp. 63-68.
    • (1992) Proc. ISSAC '92 Berkeley , pp. 63-68
    • Reid, G.J.1    Lisle, I.G.2    Boulton, A.3    Wittkopf, A.D.4
  • 73
    • 0030364642 scopus 로고    scopus 로고
    • Reduction of systems of nonlinear partial differential equations to simplified involutive forms
    • G.J. Reid, A.D. Wittkopf, A. Boulton, Reduction of systems of nonlinear partial differential equations to simplified involutive forms, Eur. J. Appl. Math. 7 (1996) 604-635.
    • (1996) Eur. J. Appl. Math. , vol.7 , pp. 604-635
    • Reid, G.J.1    Wittkopf, A.D.2    Boulton, A.3
  • 75
    • 0030717962 scopus 로고    scopus 로고
    • Rankings of Partial Derivatives
    • W. Küchlin, ed., ACM Press, New York
    • C.J. Rust, G.J. Reid, Rankings of Partial Derivatives, in: W. Küchlin, ed., Proc. ISSAC '97 (ACM Press, New York, 1997) 9-16.
    • (1997) Proc. ISSAC '97 , pp. 9-16
    • Rust, C.J.1    Reid, G.J.2
  • 76
    • 0346387642 scopus 로고
    • Coupled evolution equations for axially inhomogeneous optical fibres
    • E. Ryder, D.F. Parker, Coupled evolution equations for axially inhomogeneous optical fibres, IMA J. Appl. Math. 49 (1992) 293-309.
    • (1992) IMA J. Appl. Math. , vol.49 , pp. 293-309
    • Ryder, E.1    Parker, D.F.2
  • 77
    • 36149031438 scopus 로고
    • Painlevé analysis and integrability of coupled nonlinear Schrödinger equations
    • R. Sahadevan, K.M. Tamizhmani, M. Lakshmanan, Painlevé analysis and integrability of coupled nonlinear Schrödinger equations, J. Phys. A 19 (1986) 1783-1791.
    • (1986) J. Phys. A , vol.19 , pp. 1783-1791
    • Sahadevan, R.1    Tamizhmani, K.M.2    Lakshmanan, M.3
  • 78
    • 5544280031 scopus 로고    scopus 로고
    • Symmetries and solutions of the vector nonlinear Schrödinger equation
    • A. Sciarro, P. Winternitz, Symmetries and solutions of the vector nonlinear Schrödinger equation, Nuovo Cimento B 112 (1997) 853-871.
    • (1997) Nuovo Cimento B , vol.112 , pp. 853-871
    • Sciarro, A.1    Winternitz, P.2
  • 80
    • 11644266903 scopus 로고
    • Dynamics of coupled solitons in nonlinear optical fibers
    • T. Ueda, W.L. Kath, Dynamics of coupled solitons in nonlinear optical fibers, Phys. Rev. A 42 (1990) 563-571.
    • (1990) Phys. Rev. A , vol.42 , pp. 563-571
    • Ueda, T.1    Kath, W.L.2
  • 81
    • 0001076665 scopus 로고
    • Dynamics of optical pulses in randomly birefringent fibers
    • T. Ueda, W.L. Kath, Dynamics of optical pulses in randomly birefringent fibers, Physica D 55 (1992) 166-181.
    • (1992) Physica D , vol.55 , pp. 166-181
    • Ueda, T.1    Kath, W.L.2
  • 82
    • 0011644296 scopus 로고
    • Symmetries of compatibility conditions for systems of differential equations
    • E.M. Vorob'ev, Symmetries of compatibility conditions for systems of differential equations, Acta Appl. Math. 26 (1992) 61-86.
    • (1992) Acta Appl. Math. , vol.26 , pp. 61-86
    • Vorob'ev, E.M.1
  • 83
    • 36749112076 scopus 로고
    • The Painlevé property for partial differential equations
    • J. Weiss, M. Tabor, G. Carnevale, The Painlevé property for partial differential equations, J. Math. Phys. 24 (1983) 522-526.
    • (1983) J. Math. Phys. , vol.24 , pp. 522-526
    • Weiss, J.1    Tabor, M.2    Carnevale, G.3
  • 84
    • 0000903345 scopus 로고    scopus 로고
    • The program CRACK for solving PDEs in General Relativity
    • F.W. Hehl, R.A. Puntigam, H. Ruder, eds. Springer, Berlin
    • T. Wolf, The program CRACK for solving PDEs in General Relativity, in: Relativity and Scientific Computing: Computer Algebra, Numerics, Visualization, F.W. Hehl, R.A. Puntigam, H. Ruder, eds. (Springer, Berlin, 1996) 241-258.
    • (1996) Relativity and Scientific Computing: Computer Algebra, Numerics, Visualization , pp. 241-258
    • Wolf, T.1
  • 85
    • 0000981501 scopus 로고
    • To the integrability of the system of two coupled nonlinear Schrödinger equations
    • V.E. Zakharov, E.I. Schulman, To the integrability of the system of two coupled nonlinear Schrödinger equations, Physica D 4 (1982) 270-274.
    • (1982) Physica D , vol.4 , pp. 270-274
    • Zakharov, V.E.1    Schulman, E.I.2
  • 86
    • 0002557939 scopus 로고
    • Exact theory of two-dimensional self-focusing and one-dimensional of waves in nonlinear media
    • V.E. Zakharov, A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional of waves in nonlinear media, Sov. Phys. JETP 34 (1972) 62-69.
    • (1972) Sov. Phys. JETP , vol.34 , pp. 62-69
    • Zakharov, V.E.1    Shabat, A.B.2


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