Solution of a nonisospectral and variable coefficient Korteweg-de Vries equation
A new type of KdV equation with a nonisospectral Lax pair as well as variable coefficients is introduced. Its Lax pair is shown to be invariant under the Crum transformation. This leads to a Bäcklund transformation for the KdV equation and, hence, a method for solutions via an associated nonisospectral variable coefficients MKdV equation. Three generations of solutions are given. The 1-soliton solution shares the novel phenomenology associated with the boomeron, trappon, and zoomeron of Calogero and Degasperis.
scientific article; zbMATH DE number 4071546