Transformations and multi-solitonic solutions for a generalized variable-coefficient KadomtsevPetviashvili equation
KadomtsevPetviashvili equations with variable coefficients can be used to characterize many nonlinear phenomena in fluid dynamics and plasma physics more realistically than the equations with constant coefficients. Hereby, a generalized variable-coefficient KadomtsevPetviashvili equation with nonlinearity, dispersion and perturbed terms is investigated. Transformations, of which the consistency conditions are exactly the Painlev integrability conditions, to the Kortewegde Vries equation, cylindrical Kortewegde Vries equation, KadomtsevPetviashvili equation and cylindrical KadomtsevPetviashvili equation are presented by formal dependent variable transformation assumptions. Using the Hirota bilinear method, from the variable-coefficient bilinear equation, the multi-solitonic solution, auto-Bcklund transformation and Lax pair for the variable-coefficient KadomtsevPetviashvili equation are obtained. Moreover, the influence of inhomogeneity coefficients on solitonic structures and interaction properties is discussed for physical interest and possible applications.
multi-solitonic solution generalized variable-coefficient kadomtsevpetviashvili equation dependent variable transformation hirota bilinear method