Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method

Abstract

We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e. classes of solutions particularly stable under the nonlinear interaction. The existence of such solutions represents one of the different aspects of the property of integrability, and it can be connected to the existence of a Bäcklund transformation from which a nonlinear superposition formula can be established.