Elliptic waves in two-component long-wave–short-wave resonance interaction system in one and two dimensions

Abstract

We consider - and -dimensional long-wave–short-wave resonance interaction systems. We construct an extensive set of exact periodic solutions of these systems in terms of Lamé polynomials of order one and two. The periodic solutions are classified into three categories as similar, mixed, superposed elliptic solutions. We also discuss the hyperbolic solutions as limiting cases.