Bilinear Bäcklund transformation, N‐soliton, and infinite conservation laws for Lax–Kadomtsev–Petviashvili and generalized Korteweg–de Vries equations

Abstract

In this paper, we obtain the bilinear form for the Lax–Kadomtsev–Petviashvili (Lax–KP) and the generalized (3 + 1)‐dimensional Korteweg–de Vries equations based on the binary Bell polynomials. Accordingly, N‐soliton solutions, bilinear Bäcklund transformation, Lax pair, and infinite conservation laws will be constructed to Lax–KP and the generalized (2 + 1)‐dimensional Korteweg–de Vries equation ()false(2+1false)G−KdV. At the same time, we get another bilinear Bäcklund transformation. Finally, exact solutions were obtained by using the exchange formulas for Hirota's bilinear operators.

Multisoliton and general Wronskian solutions of a variable‐coefficient Korteweg–de Vries equation

“…Based on Hirota bilinear equation, the Wronskian technique is another powerful method for finding exact solutions. Besides multisoliton solutions, many other kinds of solutions can also be expressed in terms of Wronskian determinants, such as multirational solutions, multipositon solutions, multinegaton solutions, multicomplexiton solutions, and mixed solutions [16][17][18][19].…”