Hirota, Ryogo A new form of Bäcklund transformations and its relation to the inverse scattering problem. (English) Zbl 1168.37322 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. Cited in 130 Documents 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) PDF BibTeX XML Cite \textit{R. Hirota}, Prog. Theor. Phys. 52, 1498--1512 (1974; Zbl 1168.37322) Full Text: DOI OpenURL