Steady gap solitons in a coupled Korteweg–de Vries system: A dynamical systems approach

Abstract

In this article we search for steady gap soliton solutions of a set of coupled Korteweg–de Vries equations. These solutions arise whenever there is a narrow gap in the linear spectrum. For small amplitudes we use a dynamical systems approach combined with a normal form analysis to find a canonical equation set. When truncated at the cubic order in amplitude we can exhibit explicit solutions which agree with those found earlier by an asymptotic analysis. We argue that two of these solutions persist under perturbation by the higher-order terms.