A simple direct method to find equivalence transformations of a generalized nonlinear Schrödinger equation and a generalized KdV equation

A simple direct method is presented to find equivalence transformations of nonlinear mathematical physics equations. By using the direct method, we obtain the continuous equivalence transformations of a class of nonlinear Schröequations with variable coefficients and a family of nonlinear KdV equati...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-01, Vol.215 (10), p.3509-3514
Main Authors: Tian, Ying-hui, Chen, Han-lin, Liu, Xi-qiang
Format: Article
Language:English
Subjects:
02.03.Jr
02.20.Sv
02.20.Tw
Equivalence transformation
Exact sciences and technology
Generalized KdV equation
Generalized nonlinear Schröequation
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Sciences and techniques of general use
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Summary:A simple direct method is presented to find equivalence transformations of nonlinear mathematical physics equations. By using the direct method, we obtain the continuous equivalence transformations of a class of nonlinear Schröequations with variable coefficients and a family of nonlinear KdV equations with variable coefficients. For the nonlinear Schrödinger equations with variable coefficients, the equivalence transformations obtained by the direct method coincide, in nature, with those obtained via the infinitesimal Lie criterion, but our computation is much simpler.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2009.10.046