Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices

Abstract

Exact N‐soliton solutions have been obtained for the nonlinear waveequation ∂2 w/∂t 2 − ∂2 w/∂x 2 − 6(∂2 w 2/x 2) − ∂4 w/∂x 4 = 0 which describes motions of long waves in one‐dimensional nonlinear lattices and in shallow‐water under gravity. The solutions have the same functional form as N‐solition solutions of the Korteweg‐de Vries equation.