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Beyond Nonlinear Schrödinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range Interaction

D. Grecu·Anca Visinescu·A. S. Carstea
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Abstract

Multi scales method is used to analyze a nonlinear differential-difference equation. In order $ε^3$ the NLS equation is found to determine the space-time evolution of the leading amplitude. In the next order this has to satisfy a complex mKdV equation (the next in the NLS hierarchy) in order to eliminate secular terms. The zero dispersion point case is also analyzed and the relevant equation is a modified NLS equation with a third order derivative term included

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D. Grecu, Anca Visinescu, A. S. Carstea. 1999-10-15. Beyond Nonlinear Schrödinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range Interaction. https://arxiv.org/abs/solv-int/9910006

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