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Volumn 13, Issue 1, 2006, Pages 50-63

Construction of special solutions for nonintegrable systems

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EID: 32244440326     PISSN: 14029251     EISSN: 14029251     Source Type: Journal    
DOI: 10.2991/jnmp.2006.13.1.5     Document Type: Article
Times cited : (4)

References (53)
  • 1
    • 51249180884 scopus 로고
    • Nonlinear evolution equations and ordinary differential equations of Painlevé type
    • Ablowitz M J, Ramani A and Segur H, Nonlinear evolution equations and ordinary differential equations of Painlevé type, Lett. Nuovo Cimenta 23 (1978), 333-338;
    • (1978) Lett. Nuovo Cimenta , vol.23 , pp. 333-338
    • Ablowitz, M.J.1    Ramani, A.2    Segur, H.3
  • 2
    • 36749106124 scopus 로고
    • A connection between nonlinear evolution equations and ordinary differential equations of P-type. i & II
    • A connection between nonlinear evolution equations and ordinary differential equations of P-type. I & II, J. Math. Phys. 21 (1980), 715-721, & 1006-1015.
    • (1980) J. Math. Phys. , vol.21 , pp. 715-721
  • 3
    • 32244440563 scopus 로고
    • Simple trajectories in the rotation-symmetrical gravitational field
    • Antonov V A and Timoshkova E I, Simple trajectories in the rotation-symmetrical gravitational field, Russ. Astron. J. 70 (1993), 265-276.
    • (1993) Russ. Astron. J. , vol.70 , pp. 265-276
    • Antonov, V.A.1    Timoshkova, E.I.2
  • 6
    • 32244431652 scopus 로고
    • Theórie des fonctions elliptiques. Deuxiéme édition
    • Gauthier-Villars, Imprimeur-Libraire, Paris
    • Briot C A A and Bouquet J C, Theórie des fonctions elliptiques. Deuxiéme édition, Gauthier-Villars, Imprimeur-Libraire, Paris, 1875. On-line version: The Cornell Library Hist. Math. Monographs, http://historical.library.Cornell.edu/
    • (1875) On-line Version: The Cornell Library Hist. Math. Monographs
    • Briot, C.A.A.1    Bouquet, J.C.2
  • 7
    • 0347792330 scopus 로고
    • On the analytic structure of the Hénon-Heiles system
    • Chang Y F, Tabor M, Weiss J and Corliss G, On the Analytic Structure of the Hénon-Heiles System, Phys. Lett. A 85 (1981), 211-213.
    • (1981) Phys. Lett. A , vol.85 , pp. 211-213
    • Chang, Y.F.1    Tabor, M.2    Weiss, J.3    Corliss, G.4
  • 8
    • 36749106140 scopus 로고
    • Analytic structure of the Hénon-Heiles Hamiltonian in integrable and nonintegrable regimes
    • Chang Y F, Tabor M and Weiss J, Analytic Structure of the Hénon-Heiles Hamiltonian in integrable and nonintegrable regimes, J. Math. Phys. 23 (1982), 531-538.
    • (1982) J. Math. Phys. , vol.23 , pp. 531-538
    • Chang, Y.F.1    Tabor, M.2    Weiss, J.3
  • 9
    • 21144479106 scopus 로고
    • Link between solitary waves and projective Riccati equations
    • Conte R and Musette M, Link between solitary waves and projective Riccati equations, J. Phys. A 25 (1992), 5609-5623.
    • (1992) J. Phys. A , vol.25 , pp. 5609-5623
    • Conte, R.1    Musette, M.2
  • 10
    • 31044450316 scopus 로고
    • Linearity inside nonlinearity: Exact solutions to the complex Ginzburg-Landau equation
    • Conte R and Musette M, Linearity inside nonlinearity: exact solutions to the complex Ginzburg-Landau equation, Physica D 69 (1993), 1-17.
    • (1993) Physica D , vol.69 , pp. 1-17
    • Conte, R.1    Musette, M.2
  • 12
    • 27844565225 scopus 로고    scopus 로고
    • Explicit integration of the Hénon-Heiles Hamiltonians
    • [arXiv:nlin.SI/0412057]
    • Conte R, Musette M and Verhoeven C, Explicit integration of the Hénon-Heiles Hamiltonians, J. of Nonlin. Math. Phys. 12 (Supplement 1) (2005), 212-227 [arXiv:nlin.SI/0412057].
    • (2005) J. of Nonlin. Math. Phys. , vol.12 , Issue.1 SUPPL. , pp. 212-227
    • Conte, R.1    Musette, M.2    Verhoeven, C.3
  • 14
    • 33744717939 scopus 로고    scopus 로고
    • Modeling the fifth dimension with scalars and gravity
    • [arXiv:hep-th/9909134]
    • DeWolfe O, Freedman D Z, Gubser S S and Karch A, Modeling the fifth dimension with scalars and gravity, Phys. Rev. D 62 (2000), 046008 [arXiv:hep-th/9909134].
    • (2000) Phys. Rev. D , vol.62 , pp. 046008
    • DeWolfe, O.1    Freedman, D.Z.2    Gubser, S.S.3    Karch, A.4
  • 16
    • 0008769343 scopus 로고    scopus 로고
    • Four-dimensional gravity on a thick domain wall
    • [arXiv:hep-th/9912060]
    • Gremm M, Four-dimensional gravity on a thick domain wall, Phys. Lett. B 478 (2000), 434-438 [arXiv:hep-th/9912060];
    • (2000) Phys. Lett. B , vol.478 , pp. 434-438
    • Gremm, M.1
  • 17
    • 4243593526 scopus 로고    scopus 로고
    • Thick domain walls and singular spaces
    • [arXiv:hep-th/0002040]
    • Thick domain walls and singular spaces, Phys. Rev. D 62 (2000), 044017 [arXiv:hep-th/0002040].
    • (2000) Phys. Rev. D , vol.62 , pp. 044017
  • 18
    • 0004413317 scopus 로고    scopus 로고
    • Exact periodic steady solutions for nonlinear wave equations: A new approach
    • Grimshaw R and Pavlov M, Exact periodic steady solutions for nonlinear wave equations: A new approach, Phys. Lett. A 251 (1999), 25-30.
    • (1999) Phys. Lett. A , vol.251 , pp. 25-30
    • Grimshaw, R.1    Pavlov, M.2
  • 19
    • 0038759689 scopus 로고    scopus 로고
    • An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolutions equations
    • Fan E, An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolutions equations, J. of Phys. A 36 (2003), 7009-7026.
    • (2003) J. of Phys. A , vol.36 , pp. 7009-7026
    • Fan, E.1
  • 20
    • 32244435574 scopus 로고
    • Gesammelte mathematische Werke von L. Fuchs
    • Hrsg. von Richard Fuchs und Ludwig Schlesinger, Berlin, Mayer & Müller
    • von Fuchs L, Gesammelte mathematische Werke von L. Fuchs. Hrsg. von Richard Fuchs und Ludwig Schlesinger, Berlin, Mayer & Müller, 1904-1909. On-line version: The Cornell Library of Historical Mathematics Monographs; http : //historical.library.cornell.edu/
    • (1904) On-line Version: The Cornell Library of Historical Mathematics Monographs
    • Von Fuchs, L.1
  • 21
    • 0002519122 scopus 로고
    • The applicability of the third integral of motion: Some numerical experiments
    • Hénon M. and Heiles C., The applicability of the third integral of motion: some numerical experiments, Astron. J. 69 (1964), 73-79.
    • (1964) Astron. J. , vol.69 , pp. 73-79
    • Hénon, M.1    Heiles, C.2
  • 23
    • 19944371736 scopus 로고    scopus 로고
    • Non-existence of elliptic travelling wave solutions of the complex Ginzburg-Landau equation
    • Hone A N W, Non-existence of elliptic travelling wave solutions of the complex Ginzburg-Landau equation, Physica D 205 (2005), 292-306.
    • (2005) Physica D , vol.205 , pp. 292-306
    • Hone, A.N.W.1
  • 27
    • 0040481126 scopus 로고    scopus 로고
    • Gravitational waves from the Hénon-Heiles system
    • Kokubun F, Gravitational waves from the Hénon-Heiles system, Phys. Rev. D 57 (1998), 2610-2612.
    • (1998) Phys. Rev. D , vol.57 , pp. 2610-2612
    • Kokubun, F.1
  • 28
    • 34250579023 scopus 로고
    • Sur le problème de la rotation d'un corps solide autour d'un point fixe
    • Kowalevski S, Sur le problème de la rotation d'un corps solide autour d'un point fixe, Acta Mathematica 12 (1889), 177-232;
    • (1889) Acta Mathematica , vol.12 , pp. 177-232
    • Kowalevski, S.1
  • 29
    • 34250581889 scopus 로고
    • Sur une properiété du systéme d'équations différentielles qui définit la rotation d'un corps solide autour d'un point fixe
    • {in French}
    • Sur une properiété du systéme d'équations différentielles qui définit la rotation d'un corps solide autour d'un point fixe, Acta Mathematica 14 (1890), 81-93, {in French}.
    • (1890) Acta Mathematica , vol.14 , pp. 81-93
  • 30
    • 32244434739 scopus 로고
    • Reprinted in: AS USSR Publ. House, Moscow, {in Russian}
    • Reprinted in: Kovalevskaya S V, Scientific Works, AS USSR Publ. House, Moscow, 1948, {in Russian}.
    • (1948) Scientific Works
    • Kovalevskaya, S.V.1
  • 31
    • 10044227192 scopus 로고    scopus 로고
    • Traveling wave solutions of the Camassa-Holm Korteweg-de vries equations
    • Lenells J, Traveling Wave Solutions of the Camassa-Holm and Korteweg-de Vries Equations, J. of Nonlin. Math. Phys. 11 (2004), 508-520.
    • (2004) J. of Nonlin. Math. Phys. , vol.11 , pp. 508-520
    • Lenells, J.1
  • 32
    • 0347162180 scopus 로고    scopus 로고
    • Psi-series solutions of the cubic Hénon-Heiles system and their convergence
    • [arXiv:math.DS/9904186]
    • Melkonian S, Psi-series solutions of the cubic Hénon-Heiles system and their convergence, J. Nonlin. Math. Phys. 6 (1999), 139-160 [arXiv:math.DS/9904186],
    • (1999) J. Nonlin. Math. Phys. , vol.6 , pp. 139-160
    • Melkonian, S.1
  • 33
    • 0038009288 scopus 로고    scopus 로고
    • Analytic solitary waves of nonintegrable equations
    • arXiv:nlin.PS/0302051
    • Musette M and Conte R, Analytic solitary waves of nonintegrable equations, Physica D 181 (2003) 70-79 [arXiv:nlin.PS/0302051.
    • (2003) Physica D , vol.181 , pp. 70-79
    • Musette, M.1    Conte, R.2
  • 37
    • 4243859076 scopus 로고    scopus 로고
    • Chaos in pp-wave spacetime
    • Podolský Ji and Veselý K, Chaos in pp-wave spacetime, Phys. Rev. D 58 (1998), 081501.
    • (1998) Phys. Rev. D , vol.58 , pp. 081501
    • Podolský, Ji.1    Veselý, K.2
  • 38
    • 0000346840 scopus 로고    scopus 로고
    • Some general periodic solutions to coupled nonlinear Schrödenger equations
    • Porubov A V and Parker D F, Some general periodic solutions to coupled nonlinear Schrödenger equations, Wave Motion 29 (1999), 97-109.
    • (1999) Wave Motion , vol.29 , pp. 97-109
    • Porubov, A.V.1    Parker, D.F.2
  • 39
    • 0242679852 scopus 로고
    • Application of finite expansion in elliptic functions to solve differential eduations
    • Santos G S, Application of Finite Expansion in Elliptic Functions to Solve Differential Eduations, J. of the Physical Society of Japan 58 (1989), 4301-4310.
    • (1989) J. of the Physical Society of Japan , vol.58 , pp. 4301-4310
    • Santos, G.S.1
  • 40
    • 27844516986 scopus 로고    scopus 로고
    • A new class of trajectories of motion in the Hénon-Heiles potential field
    • {in Russian}
    • Timoshkova E I, A New class of trajectories of motion in the Hénon-Heiles potential field, Astron. Zh. 76 (1999), 470-475 {in Russian};
    • (1999) Astron. Zh. , vol.76 , pp. 470-475
    • Timoshkova, E.I.1
  • 41
    • 0033244205 scopus 로고    scopus 로고
    • {in English}
    • Astron. Rep., 43 (1999), 406-411, {in English}.
    • (1999) Astron. Rep. , vol.43 , pp. 406-411
  • 43
    • 0035981840 scopus 로고    scopus 로고
    • Integration of a generalized Hénon-Heiles Hamiltonian
    • arXiv:nlin.SI/0112030
    • Verhoeven C, Musette M and Conte R, Integration of a generalized Hénon-Heiles Hamiltonian, J. Math. Phys. 43 (2002), 1906-1915 [arXiv:nlin.SI/0112030.
    • (2002) J. Math. Phys. , vol.43 , pp. 1906-1915
    • Verhoeven, C.1    Musette, M.2    Conte, R.3
  • 44
    • 32244435206 scopus 로고    scopus 로고
    • General solution for Hamiltonians with extended cubic and quadric potentials
    • {in Russian}
    • Verhoeven C, Musette M and Conte R, General solution for Hamiltonians with extended cubic and quadric potentials, Tear. Mat. Fiz. 134 (2003), 148-159 {in Russian},
    • (2003) Tear. Mat. Fiz. , vol.134 , pp. 148-159
    • Verhoeven, C.1    Musette, M.2    Conte, R.3
  • 45
    • 0037236205 scopus 로고    scopus 로고
    • {in English} [arXiv:nlin.SI/0301011]
    • Theor. Math. Phys. 134 (2003), 128 {in English} [arXiv:nlin.SI/0301011],
    • (2003) Theor. Math. Phys. , vol.134 , pp. 128
  • 46
    • 0037865558 scopus 로고    scopus 로고
    • Constructing solutions for the generalized Hénon-Heiles system through the Painlevé test
    • {in Russian}
    • Vernov S Yu, Constructing solutions for the generalized Hénon-Heiles system through the Painlevé test, Tear. Mat. Fiz. 135 (2003), 409-419 {in Russian},
    • (2003) Tear. Mat. Fiz. , vol.135 , pp. 409-419
    • Vernov, S.Yu.1
  • 47
    • 0037865558 scopus 로고    scopus 로고
    • {in English} [arXiv:math-ph/0209063]
    • Theor. Math. Phys. 135 (2003), 792-801 {in English} [arXiv:math-ph/ 0209063].
    • (2003) Theor. Math. Phys. , vol.135 , pp. 792-801
  • 48
    • 31044436413 scopus 로고    scopus 로고
    • Construction of single-valued solutions for nonintegrable systems with the help of the painlevé test
    • Editors: Ganzha V G, Mayr E W and Vorozhtsov E V, Technische Universitat, Munchen, Garching, [arXiv:nlin.SI/0407062]
    • Vernov S Yu, Construction of Single-valued Solutions for Nonintegrable Systems with the Help of the Painlevé Test, in: Proc. of the International Conference "Computer Algebra in Scientific Computing" (CASC'04, St. Petersburg, Russia, 2004), Editors: Ganzha V G, Mayr E W and Vorozhtsov E V, Technische Universitat, Munchen, Garching, 2004, 457-465 [arXiv:nlin.SI/0407062].
    • (2004) Proc. of the International Conference "Computer Algebra in Scientific Computing" (CASC'04, St. Petersburg, Russia, 2004) , pp. 457-465
    • Vernov, S.Yu.1
  • 51
    • 0009125464 scopus 로고
    • Bäcklund transformation and linearizations of the Hénon-Heiles system
    • Weiss J, Bäcklund Transformation and Linearizations of the Hénon-Heiles System, Phys. Lett. A 102 (1984), 329-331.
    • (1984) Phys. Lett. A , vol.102 , pp. 329-331
    • Weiss, J.1
  • 52
    • 0000532111 scopus 로고
    • Backhand transformation and the Hénon-Heiles system
    • Weiss J, Backhand Transformation and the Hénon-Heiles System, Phys. Lett. A 105 (1984), 387-389.
    • (1984) Phys. Lett. A , vol.105 , pp. 387-389
    • Weiss, J.1
  • 53
    • 14144251108 scopus 로고    scopus 로고
    • The extended Fan's sub-equation method and its application to KdV-MkdV, BKK and variant Boussinesq equations
    • Yomba E, The extended Fan's sub-equation method and its application to KdV-MkdV, BKK and variant Boussinesq equations, Phys Lett. A 336 (2005), 463-476.
    • (2005) Phys Lett. A , vol.336 , pp. 463-476
    • Yomba, E.1


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