Transformations and multi-solitonic solutions for a generalized variable-coefficient Kadomtsev-Petviashvili equation. (English) Zbl 1222.35177
Summary: Kadomtsev-Petviashvili 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 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 equation, cylindrical Korteweg-de Vries equation, Kadomtsev-Petviashvili equation and cylindrical Kadomtsev-Petviashvili 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-Bäcklund transformation and Lax pair for the variable-coefficient Kadomtsev-Petviashvili equation are obtained. Moreover, the influence of inhomogeneity coefficients on solitonic structures and interaction properties is discussed for physical interest and possible applications.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C08 | Soliton solutions |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
Keywords:
generalized variable-coefficient Kadomtsev-Petviashvili equation; dependent variable transformation; Hirota bilinear method; multi-solitonic solutionReferences:
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