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Approximation of the DNLS equation by the cubic nonlinear Schrödinger equation

Author： Oliveira Filipe

Publisher： Royal Society of Edinburgh

ISSN： 1473-7124

Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.134, Iss.3, 2004-06, pp. : 595-607

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

We rigorously approach the Schr¨odinger equation of derivative type q_t + i q_xx + λ |q|² q_x + μq² ¯ q_x = 0, λ ∈ R, μ ∈ C, by the cubic nonlinear Schr¨odinger equation A_T + i A_XX + i k₀ ( λ − μ) | A |² A = 0. We also study the case of the KdV-like equation q_t + i q_xx + aq_xxx + i |q|² q + ~ λ (|q|² q)_x + ~ μ |q|² q_x = 0, ~λ,~ μ ∈ R, arising in optical physics.

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