Relationships among inverse method, Bäcklund transformation and an infinite number of conservation laws. (English) Zbl 1079.35506

Wadati, Miki; Sanuki, Heiji; Konno, Kimiaki

Prog. Theor. Phys. 53, 419-436 (1975).

Summary: It is shown that the inverse method, the Bäcklund transformation and an infinite number of conservation laws are closely related. The derivation of the Bäcklund transformation from the fundamental equations of the inverse method is explicitly shown. Also it is shown that the conservation law is obtained in a simple way from the Riccati form of the inverse method and the derivation of the conservation law from the Bäcklund transformation is possible.

MSC:

35A30	Geometric theory, characteristics, transformations in context of PDEs
37K35	Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35L67	Shocks and singularities for hyperbolic equations