Two topics of the integrable soliton equation
I summarize some results obtained recently. The first topic is the breaking soliton equations in \(2+ 1\)-dimensional case. Some typical equations are deduced from the nonisospectral zero curvature equation. The Darboux transformations can be used to find the breaking soliton solutions of these equations, the algebraic properties of them are also considered. The second topic is the separation of variables for the soliton equations by constraints via Lax pair. The motivation of this topic is in the discovery of the similarity of the Fourier analysis and superposition rule for linear equations and the nonlinear Fourier analysis and nonlinear superposition for soliton equations.
nonlinear superposition for soliton equations
scientific article; zbMATH DE number 907329
scientific article