Group-invariant solutions of the (2+1)-dimensional cubic Schrödinger equation

C. Özemir; F. Güngör

doi:10.1088/0305-4470/39/12/008

Group-invariant solutions of the (2+1)-dimensional cubic Schrödinger equation

C. Özemir^*, F. Güngör

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Technical University

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We use Lie point symmetries of the (2+1)-dimensional cubic Schrödinger equation to obtain new analytic solutions in a systematic manner. We present an analysis of the reduced ODEs, and in particular show that although the original equation is not integrable they typically can belong to the class of Painlevé-type equations.

Original language	English
Pages (from-to)	2973-2993
Number of pages	21
Journal	Journal of Physics A: Mathematical and General
Volume	39
Issue number	12
DOIs	https://doi.org/10.1088/0305-4470/39/12/008
Publication status	Published - 24 Mar 2006

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title = "Group-invariant solutions of the (2+1)-dimensional cubic Schr{\"o}dinger equation",

abstract = "We use Lie point symmetries of the (2+1)-dimensional cubic Schr{\"o}dinger equation to obtain new analytic solutions in a systematic manner. We present an analysis of the reduced ODEs, and in particular show that although the original equation is not integrable they typically can belong to the class of Painlev{\'e}-type equations.",

author = "C. {\"O}zemir and F. G{\"u}ng{\"o}r",

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AU - Güngör, F.

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N2 - We use Lie point symmetries of the (2+1)-dimensional cubic Schrödinger equation to obtain new analytic solutions in a systematic manner. We present an analysis of the reduced ODEs, and in particular show that although the original equation is not integrable they typically can belong to the class of Painlevé-type equations.

AB - We use Lie point symmetries of the (2+1)-dimensional cubic Schrödinger equation to obtain new analytic solutions in a systematic manner. We present an analysis of the reduced ODEs, and in particular show that although the original equation is not integrable they typically can belong to the class of Painlevé-type equations.

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 12

ER -

Group-invariant solutions of the (2+1)-dimensional cubic Schrödinger equation

Abstract

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