HODOGRAPH-TYPE TRANSFORMATIONS RELATING TO INTEGRABLE EQUATIONS

Hodograph-type transformations are the point transformations that the new independent and dependent variables depend respectively on the old dependent and independent variables. In this paper, a class of hodograph-type transformations of the form x' = P(t,u),t' = Q(t),u' = R(x,t) are...

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Published inPacific journal of applied mathematics Vol. 3; no. 1/2; p. 111
Main Authors Kang, Jing, Qu, Changzheng
Format Journal Article
LanguageEnglish
Published Hauppauge Nova Science Publishers, Inc 01.01.2011
Subjects
Dependent variables
Independent variables
Linear equations
Mathematical analysis
Nonlinear equations
Nonlinear evolution equations
Partial differential equations
Transformations
Transformations (mathematics)
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ISSN1941-3963

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Summary:Hodograph-type transformations are the point transformations that the new independent and dependent variables depend respectively on the old dependent and independent variables. In this paper, a class of hodograph-type transformations of the form x' = P(t,u),t' = Q(t),u' = R(x,t) are used to connect the nonlinear evolution equations of the form u^sub t^ =F(x,t,u,u^sub 1^,···,u^sub n^),u^sub n^ =∂^sup n^u/∂x^sup n^,n=2,3,4,5 with linear equations of the form ... and the third-order (n = 3) and fifth-order (n = 5) equations with some known third-order C-integrable and fifth-order symmetry-integrable equations, respectively. Such nonlinear equations based on hodograph-type transformations are completely classified .
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ISSN:1941-3963