The integrability for a generalized seventh-order KdV equation: Painlevé property, soliton solutions, Lax pairs and conservation laws

Abstract

This paper investigates the integrability of a generalized seventh-order Korteweg–de Vries equation arising in fluids and plasmas. By means of singularity structure analysis, it is proven that this equation passes the Painlevé test for integrability in only three distinct cases. Under three sets of Painlevé integrable conditions, the soliton solutions are obtained by using Hirotaʼs bilinear method; the pseudopotentials and Lax pairs are derived by virtue of the method developed by Nucci. Finally, the infinite conservation laws are found by using its Lax pair, and all conserved densities and fluxes are presented with explicit recursion formulas.