Elliptic Waves in Two Component Long Wave--Short Wave Resonance Interaction System in One and Two dimensions

TL;DR

This paper constructs and classifies exact periodic solutions for (2+1) and (1+1) dimensional long-wave short-wave resonance systems using Lamé polynomials, including elliptic and hyperbolic solutions.

Contribution

It provides a comprehensive set of explicit periodic solutions for the resonance systems, expanding the understanding of their wave dynamics.

Findings

Classified solutions into similar, mixed, and superposed elliptic types.

Derived hyperbolic solutions as limits of elliptic solutions.

Extended the solution space for long-wave short-wave resonance systems.

Abstract

We consider (2+1) and (1+1) dimensional long-wave short-wave resonance interaction systems. We construct an extensive set of exact periodic solutions of these systems in terms of Lam\'e 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.