On the Moutard transformation for integrable partial differential equations. (English) Zbl 0737.35091
Summary: The Moutard transformation is a Darboux-type transformation appropriate to linear scattering problems of hyperbolic or elliptic type in two independent and one dependent variable. We derive this transformation, as well as the Darboux transformation for parabolic linear problems, by a ‘factorization’ method and discuss the use of compositions of such transformations in the construction of solutions to the Novikov-Veselov equations.
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
58J72 | Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds |
35P25 | Scattering theory for PDEs |