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Numerical homoclinic instabilities and the complex modified Korteweg-de Vries equation. (English) Zbl 0900.65350

65Z05Applications of numerical analysis to physics
35Q53KdV-like (Korteweg-de Vries) equations
35Q55NLS-like (nonlinear Schrödinger) equations
65M12Stability and convergence of numerical methods (IVP of PDE)
Full Text: DOI
[1] Curry, J. H.; Herring, J. R.; Loncaric, J.; Orszag, S. A.: Order and disorder in two- and three-dimensional Bénard convention. J. fluid mech. 147, 1 (1984) · Zbl 0547.76093
[2] Herbst, B. M.; Ablowitz, M. J.: Numerically induced chaos in the nonlinear Schrödinger equation. Phys. rev. Lett. 62, 2065 (1989) · Zbl 0711.35131
[3] Herbst, B. M.; Ablowitz, M. J.: On numerical chaos in the nonlinear Schrödinger equation. Lecture notes in physics 342, 192-206 (1989)
[4] Ablowitz, M. J.; Herbst, B. M.; Keiser, J. M.: Nonlinear evolution equations, solitons, chaos and cellular automata. Nonlinear physics, 166-189 (1990) · Zbl 0728.35102
[5] Ablowitz, M. J.; Herbst, B. M.: On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation. SIAM J. Appl. math. 50, 339 (1990) · Zbl 0707.35141
[6] Ablowitz, M. J.; Herbst, B. M.: On homoclinic boundaries in the nonlinear Schrödinger equation. Hamiltonian systems, transformation groups and spectral transform methods, 121-131 (1990) · Zbl 0736.35105
[7] Stuart, J. T.; Diprima, R. C.: The eckhaus and benjamin-feir resonance mechanisms. Proc. R. Soc. London A 362, 27 (1978)
[8] Ablowitz, M. J.; Segur, H.: Solitons and the inverse scattering transform. (1981) · Zbl 0472.35002
[9] Hirota, R.: Direct methods of finding exact solutions of nonlinear evolution equations. Lecture notes in mathematics 515 (1976) · Zbl 0336.35024
[10] Guckenheimer, J.; Holmes, P.: Nonlinear oscillations, dynamical systems and bifurcations of vector fields. (1983) · Zbl 0515.34001
[11] Wiggens, S.: Global bifurcations and chaos. (1988)
[12] Ablowitz, M. J.; Ladik, J. F.: A nonlinear difference scheme and inverse scattering. Stud. appl. Math. 55, 213 (1976) · Zbl 0338.35002
[13] Taha, T. R.; Ablowitz, M. J.: Analytical and numerical aspects of certain nonlinear evolution equations, I. Analytical. J. comput. Phys. 55, 192 (1984) · Zbl 0541.65081
[14] . Physica D 43, 349 (1990)