On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation. (English) Zbl 0707.35141

Authors’ summary: It has recently been demonstrated that standard discretizations of the cubic nonlinear Schrödinger (NLS) equation may lead to spurious numeical behaviour. In particular, the origins of numerically induced chaos and the loss of spatial symmetry are related to the homoclinic structure associated with the NLS equation. In this paper, an analytic description of the homoclinic structure via soliton type solutions is provided and some consequences for numerical computations are demonstrated. differences between an integrable discretization and standard discretizations are highlighted.
Reviewer: A.D.Osborne


35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
35B35 Stability in context of PDEs
65Z05 Applications to the sciences
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