Matthew Russo, S. Roy Choudhury

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 generalizations of KdV equations, three variants of generalized MKdV equations, and a recently-considered nonlocal PT-symmetric NLS equation. 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. Employing the Painleve singular manifold method, some solutions are also presented for the generalized variable-coefficient integrable KdV and MKdV equations derived here. 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.

http://arxiv.org/abs/1404.4602

Mathematical Physics (math-ph)