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Volumn 27, Issue 3, 2006, Pages 759-773

Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons

Author keywords

Continuation; Optical soliton; Second harmonic generation; Type I interaction

Indexed keywords

COMPUTER SIMULATION; CONFORMAL MAPPING; NUMERICAL METHODS; OPTICAL SYSTEMS; SECOND HARMONIC GENERATION;

EID: 33644905988     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/040604455     Document Type: Article
Times cited : (11)

References (35)
  • 1
    • 6244291919 scopus 로고
    • U. ASCHER AND R. RUSSELL, EDS., Birkhäuser, Boston
    • U. ASCHER AND R. RUSSELL, EDS., Numerical Boundary Value ODEs, Birkhäuser, Boston, 1984.
    • (1984) Numerical Boundary Value ODEs
  • 2
    • 0942289311 scopus 로고    scopus 로고
    • Temporal solitons in quadratic non-linear media with opposite group-velocity dispersion at the fundamental and second harmonics
    • K. BECKWITT, Y.-F. CHEN, F. WISE, AND B. MALOMED, Temporal solitons in quadratic non-linear media with opposite group-velocity dispersion at the fundamental and second harmonics, Phys. Rev. E. 68 (2003), 057601.
    • (2003) Phys. Rev. E. , vol.68 , pp. 057601
    • Beckwitt, K.1    Chen, Y.-F.2    Wise, F.3    Malomed, B.4
  • 6
    • 0036837667 scopus 로고    scopus 로고
    • Optical solitons due to quadratic nonlinearities: From, basic physics to futuristic applications
    • A. V. BURYAK, P. D. TRAPANI, D. V. SKRYABIN, AND S. TRILLO, Optical solitons due to quadratic nonlinearities: from, basic physics to futuristic applications, Phys. Reports, 370 (2002), pp. 63-235.
    • (2002) Phys. Reports , vol.370 , pp. 63-235
    • Buryak, A.V.1    Trapani, P.D.2    Skryabin, D.V.3    Trillo, S.4
  • 9
    • 0037051411 scopus 로고    scopus 로고
    • Do true elevation solitary waves exist? A numerical investigation
    • A. CHAMPNEYS, J.-M. VANDEN-BROEK, AND G. LORD, Do true elevation solitary waves exist? A numerical investigation, J. Fluid Mech., 454 (2002), pp. 403-417.
    • (2002) J. Fluid Mech. , vol.454 , pp. 403-417
    • Champneys, A.1    Vanden-Broek, J.-M.2    Lord, G.3
  • 10
    • 8744230577 scopus 로고    scopus 로고
    • Matcont: A Matlab package for numerical bifurcation analysis of odes
    • A. DHOOGE, W. GOVAERTS, AND Y. KUZNETSOV, Matcont: A Matlab package for numerical bifurcation analysis of odes, ACM Trans. Math. Software, 29 (2003), pp. 141-164.
    • (2003) ACM Trans. Math. Software , vol.29 , pp. 141-164
    • Dhooge, A.1    Govaerts, W.2    Kuznetsov, Y.3
  • 11
    • 0000378937 scopus 로고
    • Numerical analysis and control of bifurcation problems (I) Bifurcation in finite dimensions
    • E. DOEDEL, H. B. KELLER, AND J. P. KERNEVEZ, Numerical analysis and control of bifurcation problems (I) Bifurcation in finite dimensions, Internat. J. Bifurc. Chaos Appl. Sci. Engrg., 1 (1991), pp. 493-520.
    • (1991) Internat. J. Bifurc. Chaos Appl. Sci. Engrg. , vol.1 , pp. 493-520
    • Doedel, E.1    Keller, H.B.2    Kernevez, J.P.3
  • 12
    • 0000378934 scopus 로고
    • Numerical analysis and control of bifurcation problems (II) Bifurcation in infinite dimensions
    • E. DOEDEL, H. B. KELLER, AND J. P. KERNEVEZ, Numerical analysis and control of bifurcation problems (II) Bifurcation in infinite dimensions, Internat. J. Bifurc. Chaos Appl. Sci. Engrg., 1 (1991), pp. 745-772.
    • (1991) Internat. J. Bifurc. Chaos Appl. Sci. Engrg. , vol.1 , pp. 745-772
    • Doedel, E.1    Keller, H.B.2    Kernevez, J.P.3
  • 13
    • 0026170304 scopus 로고
    • Numerical computation and continuation of invariant manifolds connecting fixed points
    • M. J. FRIEDMAN AND E. J. DOEDEL, Numerical computation and continuation of invariant manifolds connecting fixed points, SIAM J. Numer. Anal., 28 (1991), pp. 789-808.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 789-808
    • Friedman, M.J.1    Doedel, E.J.2
  • 14
    • 3743084624 scopus 로고    scopus 로고
    • Simultaneous solitary-wave solutions in a nonlinear parametric waveguide
    • H. HE, M. WERNER, AND P. DRUMMOND, Simultaneous solitary-wave solutions in a nonlinear parametric waveguide, Phys. Rev. E, 54 (1996), pp. 896-911.
    • (1996) Phys. Rev. E , vol.54 , pp. 896-911
    • He, H.1    Werner, M.2    Drummond, P.3
  • 15
    • 49049151095 scopus 로고
    • On diffraction and dispersion effect on three wave interaction
    • A. KANASHOV AND A. RUBENCHIK, On diffraction and dispersion effect on three wave interaction, Phys. D, 4 (1981), pp. 122-134.
    • (1981) Phys. D , vol.4 , pp. 122-134
    • Kanashov, A.1    Rubenchik, A.2
  • 16
    • 0003394350 scopus 로고
    • Lectures on Numerical Methods in Bifurcation Problems
    • Tata Institute of Fundamental Research, Tata Institute, Bombay, Springer-Verlag, Berlin
    • H. KELLER, Lectures on Numerical Methods in Bifurcation Problems, Tata Institute of Fundamental Research, Lectures on Mathematics and Physics 79, Tata Institute, Bombay, Springer-Verlag, Berlin, 1987.
    • (1987) Lectures on Mathematics and Physics , vol.79
    • Keller, H.1
  • 17
    • 0030621838 scopus 로고    scopus 로고
    • Computation and continuation of homoclinic and heteroclinic orbits with arclength parameterization
    • L. LIU, G. MOORE, AND R. D. RUSSELL, Computation and continuation of homoclinic and heteroclinic orbits with arclength parameterization, SIAM J. Sci. Comput., 18 (1997), pp. 69-93.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 69-93
    • Liu, L.1    Moore, G.2    Russell, R.D.3
  • 18
    • 0001628648 scopus 로고    scopus 로고
    • Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic
    • X. LIU, K. BECKWITT, AND F. WISE, Noncollinear generation of optical spatiotemporal solitons and application to ultrafast digital logic, Phys. Rev. E, 61 (2000), R4722.
    • (2000) Phys. Rev. E , vol.61
    • Liu, X.1    Beckwitt, K.2    Wise, F.3
  • 19
    • 0034225382 scopus 로고    scopus 로고
    • Two-dimensional optical spatiotemporal solitons in quadratic media
    • X. LIU, K. BECKWITT, AND F. WISE, Two-dimensional optical spatiotemporal solitons in quadratic media, Phys. Rev. E, 62 (2000), pp. 1328-1340.
    • (2000) Phys. Rev. E , vol.62 , pp. 1328-1340
    • Liu, X.1    Beckwitt, K.2    Wise, F.3
  • 20
    • 0000259557 scopus 로고    scopus 로고
    • Generation of optical spatiotemporal solitons
    • X. LIU, L. QIAN, AND F. WISE, Generation of optical spatiotemporal solitons, Phys. Rev. Lett., 82 (1999), pp. 4631-4634.
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 4631-4634
    • Liu, X.1    Qian, L.2    Wise, F.3
  • 21
    • 0000210625 scopus 로고
    • Homoclinic explosions in the complex Ginzburg-landau equation
    • B. LUCE, Homoclinic explosions in the complex Ginzburg-Landau equation, Phys. D, 84 (1995), pp. 553-581.
    • (1995) Phys. D , vol.84 , pp. 553-581
    • Luce, B.1
  • 22
    • 0001639797 scopus 로고    scopus 로고
    • An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions
    • K. LUST, D. ROOSE, A. SPENCE, AND A. R. CHAMPNEYS, An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions, SIAM J. Sci. Comput., 19 (1998), pp. 1188-1209.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1188-1209
    • Lust, K.1    Roose, D.2    Spence, A.3    Champneys, A.R.4
  • 23
    • 0000262473 scopus 로고    scopus 로고
    • Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity
    • B. A. MALOMED, P. DRUMMOND, H. HE, A. BERTSON, D. ANDERSON, AND M. LISAK, Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity, Phys. Rev. E, 56 (1997), pp. 4725-4735.
    • (1997) Phys. Rev. e , vol.56 , pp. 4725-4735
    • Malomed, B.A.1    Drummond, P.2    He, H.3    Bertson, A.4    Anderson, D.5    Lisak, M.6
  • 26
    • 85160614705 scopus 로고    scopus 로고
    • Ph.D. thesis, Engineering Mathematics, University of Bristol, Bristol, UK
    • M. J. PEARCE, Embedded Solitons in a Three-Wave System, Ph.D. thesis, Engineering Mathematics, University of Bristol, Bristol, UK, 2003.
    • (2003) Embedded Solitons in A Three-wave System
    • Pearce, M.J.1
  • 27
    • 0038347407 scopus 로고    scopus 로고
    • Continuation of periodic orbits in conservative and Hamiltonian systems
    • F. MUNOZ-ALMARAZ, E. FREIRE, J. GALÁN, E. DOEDEL, AND A. VANDERBAUWHEDE, Continuation of periodic orbits in conservative and Hamiltonian systems, Phys. D, 181 (2003), pp. 1-38.
    • (2003) Phys. D , vol.181 , pp. 1-38
    • Munoz-Almaraz, F.1    Freire, E.2    Galán, J.3    Doedel, E.4    Vanderbauwhede, A.5
  • 28
    • 0000437022 scopus 로고
    • Instability of solitons governed by quadratic nonlinearities
    • D. PELINOVSKY, A. BURYAK, AND Y. KIVSHAR, Instability of solitons governed by quadratic nonlinearities, Phys. Rev. Lett., 75 (1995), pp. 591-595.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 591-595
    • Pelinovsky, D.1    Buryak, A.2    Kivshar, Y.3
  • 30
    • 0347110869 scopus 로고    scopus 로고
    • Stability of multi-parameter solitons: Asymptotic approach
    • D. V. SKRYABIN, Stability of multi-parameter solitons: Asymptotic approach, Phys. D, 139 (2000), pp. 186-193.
    • (2000) Phys. D , vol.139 , pp. 186-193
    • Skryabin, D.V.1
  • 31
    • 0032028714 scopus 로고    scopus 로고
    • Generation and stability of optical bullets in quadratic nonlinear media
    • D. V. SKRYABIN AND W. J. FIRTH, Generation and stability of optical bullets in quadratic nonlinear media, Optics Communications, 148 (1998), pp. 79-84.
    • (1998) Optics Communications , vol.148 , pp. 79-84
    • Skryabin, D.V.1    Firth, W.J.2
  • 33
    • 0038059085 scopus 로고    scopus 로고
    • Light bullets in quadratic media with normal dispersion at the second harmonic
    • I. TOWERS, B. MALOMED, AND F. WISE, Light bullets in quadratic media with normal dispersion at the second harmonic, Phys. Rev. Lett., 90 (2003), 123902.
    • (2003) Phys. Rev. Lett. , vol.90 , pp. 123902
    • Towers, I.1    Malomed, B.2    Wise, F.3
  • 35
    • 0000405864 scopus 로고
    • Candys/qa - A software system for the qualitative analysis of nonlinear dynamical systems
    • F. ULRIKE AND J. WOLFGANG, Candys/qa - A software system for the qualitative analysis of nonlinear dynamical systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 2 (1992), pp. 773-794.
    • (1992) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.2 , pp. 773-794
    • Ulrike, F.1    Wolfgang, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.