A new form of Bäcklund transformations and its relation to the inverse scattering problem. (English) Zbl 1168.37322

Hirota, Ryogo

Prog. Theor. Phys. 52, No. 5, 1498-1512 (1974).

Summary: We present a new form of Bäcklund transformations which gives a unified method of finding Bäcklund transformations for solutions of certain nonlinear evolution equations and constructing the inverse scattering problem for solving the initial-value problem. We consider the sine-Gordon equation, the modified Korteweg-de Vries equation and the Korteweg-de Vries equation as examples.

MSC:

37K35	Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
37K15	Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
35Q53	KdV equations (Korteweg-de Vries equations)