On the Nonexistence of Soliton Solutions of the Regularized Long-Wave Equation

Abstract

The regularized long wave equation (RLW) was proposed as a model of the dynamics of long nonlinear surface waves with small amplitudes. The standard model in this domain is the Korteweg-de Vries equation (KdV) and it has been shown that these equations are predictively equivalent to the order of approximation used in their derivations. On the other hand, numerical computations indicate that the RLW has no multisoliton solutions and it is generally conjectured that it is not a soliton equation. In this paper we prove that the equation has no analytic two-soliton solutions.