Binary Bell polynomial manipulations on the integrability of a generalized (2+1) -dimensional Korteweg–de Vries equation

Abstract

This paper investigates the integrability of a generalized (2+1)-dimensional Korteweg–de Vries equation. With the aid of binary Bell polynomials, its bilinear formalism, bilinear Bäcklund transformation, Lax pair and Darboux covariant Lax pair are succinctly constructed, which can be reduced to the ones of several integrable equations such as the Korteweg–de Vries equation and the Calogero–Bogoyavlenskii–Schiff equation. Moreover, the infinite conservation laws of the generalized (2+1)-dimensional Korteweg–de Vries equation are found by virtue of binary Bell polynomials. All conserved densities and fluxes are given with explicit recursion formulas.