Bäcklund transformations for several cases of a type of generalized KdV equation (Q1777857)

Summary: An alternate generalized Korteweg-de Vries equation \[ w_t+ w_{xxx}+ g'(w_x)=0, \] where \(g(t)\) is a polynomial, is studied here. A procedure for generating solutions is given. A theorem is presented, which is subsequently applied to this equation to obtain a type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting, new, ordinary differential equations are generated and studied.