Building Generalized Lax Integrable KdV and MKdV Equations with Spatiotemporally Varying Coefficients

Physics and Mathematics of Nonlinear Phenomena 2013

Russo, M.^1 ; Choudhury, S.R.^1

Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364, United States^1

关键词: Backlund transformations;    Generalized KdV equation;    Integrable hierarchy;    Integrable systems;    Singular manifold methods;    Variable coefficients;    Variable-coefficient generalizations;    Varying coefficients;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012038/pdf
DOI  :  10.1088/1742-6596/482/1/012038

来源: IOP

【 摘 要 】

We present a technique based on extended Lax Pairs to derive variable-coefficient generalizations of various Lax-integrable NLPDE hierarchies. As illustrative examples, we consider generalized KdV equations, and three variants of generalized MKdV equations. It is demonstrated that the technique yields Lax- or S-integrable NLPDEs with both time- AND space-dependent coefficients which are thus more general than almost all cases considered earlier via other methods such as the Painleve´ Test, Bell Polynomials, and various similarity methods. Some solutions are also presented for the generalized KdV equation derived here by the use of the Painleve´ singular manifold method. Current and future work is centered on generalizing other integrable hierarchies of NLPDEs similarly, and deriving various integrability properties such as solutions, Backlund Transformations, and hierarchies of conservation laws for these new integrable systems with variable coefficients.