广义变系数Kadomtsev-Petviashvili方程的变换和多孤子型解

Kadomtsev-Petviashvili equations with variable coefficients can be used to characterize many nonlinear phenomena in fluid dynamics and plasma physics more realistically than the constant-coefficient ones. Hereby, a generalized time-dependent variable-coefficient Kadomtsev-Petviashvili equation with nonlinearity, dispersion and perturbed terms is investigated. Transformations, of which the consistency conditions are exactly the Painlevé integrability conditions, to the Korteweg-de Vries, cylindrical Korteweg-de Vries, Kadomtsev-Petviashvili and cylindrical Kadomtsev-Petviashvili equation are presented by formal dependent variable transformation assumptions. Using modified Hirota bilinear method, from the variable-coefficient bilinear equation, the multi-solitonic solution, auto-Bäcklund transformation and Lax pair for the variable-coefficient Kadomtsev-Petviashvili equation are obtained. Multi-solitonic solution in Wronskian form is also constructed and verified by the Wronskian technique. Moreover, the influences of the variable-coefficient functions and solitonic structures and interaction properties are discussed for physical interests and possible applications.