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Approximation of the DNLS equation by the cubic nonlinear Schrödinger equation

Published online by Cambridge University Press:  12 July 2007

Filipe Oliveira
Filipe Oliveira
Affiliation:
Centro de Matemática, University of Minho, Campus of Gualtar, 4710-057 Braga, Portugal
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Abstract

We rigorously approach the Schrödinger equation of derivative type qt + iqxx + λ |q|2qx + μq2q̄x = 0, λ ∈ R, μ ∈ C, by the cubic nonlinear Schrödinger equation AT + i AXX + i k0 (λ − μ) |A|2A = 0. We also study the case of the KdV-like equation qt + i qxx + aqxxx + i |q|2q + λ̃ (|q|2q)x + μ̃ |q|2qx = 0, λ̃ μ̃ ∈ R, arising in optical physics.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 3 , June 2004 , pp. 595 - 607
Copyright
Copyright © Royal Society of Edinburgh 2004

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