On an analytical method and soliton-typed solutions for certain variable-coefficient partial differential equations in nonlinear mechanics

Among the currently interesting nonlinear topics are the variable-coefficient generalizations of the Kadomtsev-Petviashvili equation (GvcKPs), which are of practical value in mechanical and physical sciences. In this note, we propose a generalized variable-coefficient tanh method with computerized symbolic manipulation for a GvcKP to construct certain soliton-typed analytical solutions. In illustration, the nearly concentric Korteweg-de Vries (KdV) equation is presented as an example, and the cylindrical KP equation as a counter example. Similar success not shown here is on the variable-coefficient KdV equations.