New bilinearization, Bäcklund transformation and infinite conservation laws for the KdV6 equation with Bell polynomials

Abstract

By using the Bell polynomials method and symbolic computation, we study the integrability of the KdV6 equation. We develop, in this work, new results regarding the integrability concept. We show that the newly developed bilinear representation and bilinear Bäcklund transformation are different from those reported in the literature. Moreover, we firstly present the infinite conservation laws, and the conserved densities and fluxes are given in explicit recursion formulas.

New exact solutions to extended (3 + 1)‐dimensional Jimbo‐Miwa equations by using bilinear forms

“…It is worth to mention that Bell polynomial approach is of great importance as it has been used to derive N‐soliton solutions for the first two nontrivial equations in the KdV6 hierarchy, bilinear forms of (2 + 1)‐dimensional KdV equation, extended (2 + 1)‐dimensional shallow water wave equation, and (2 + 1)‐dimensional Sawada‐Kotera equation . Moreover, Bäcklund transformation and infinite conservation laws, analytic properties such as the soliton solutions for two‐mode KdV equation, Bäcklund transformations, Lax system, conservation laws, and multisoliton solutions for Jimbo‐Miwa equation are explored by applying the binary Bell polynomials.…”

A Fifth-Order Korteweg-de Vries Equation for Shallow Water with Surface Tension: Multiple Soliton Solutions

“…Studies of finding soliton solutions of the nonlinear equations attracted huge number of works in a variety of fields in [19][20][21][22][23][24][25][26][27][28][29][30] and some of the references therein. Towards this goal, a variety of powerful methods to construct multiple soliton solutions has been established in the fields of mathematical physics and engineering.…”