2021•Mathematical Methods in the Applied SciencesRequires access

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

Shrouk Wael, ALY RAMADAN SEADAWY, Salah M. Moawad, Omar H. El‐Kalaawy

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 . 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.

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Key concepts: Mathematics, Conservation law, Lax pair, Bell polynomials, Bilinear interpolation, Transformation (genetics), Bilinear form, Korteweg–de Vries equation