Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-18T22:33:50.936Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)