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

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 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.

Accepted for publication in Physics Letters A. 16 pages, 8 figures

References in corpus (4)

• Instability and Evolution of Nonlinearly Interacting Water Waves
• Two-component Analogue of Two-dimensional Long Wave-Short Wave Resonance Interaction Equations: A Derivation and Solutions
• Higher dimensional bright solitons and their collisions in multicomponent long wave-short wave system
• Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations

Cited by in corpus (3)

• General Mixed Multi-Soliton Solutions to One-Dimensional Multicomponent Yajima-Oikawa System
• Higher dimensional localized and periodic wave dynamics in a new integrable (2+1)-dimensional Kundu-Mukherjee-Naskar model
• Appearing (disappearing) lumps and rogue lumps of the two-dimensional vector Yajima-Oikawa system