Two-component Analogue of Two-dimensional Long Wave-Shrot Wave Resonance Interaction Equations: A Derivation and Solutions

Recently, vector soliton equations (or coupled soliton equations) such as the vector Nonlinear Schrödinger (vNLS) equation have received so much attention in mathematical physics and nonlinear physics. Especially, the vNLS equation has been studied by several researchers from both mathematical and physical points of view [1-5]. It was pointed out that vector solitons can be used in the construction of logic gate [6-8]. It was also pointed out that Yang-Baxter map is the key to understand the mathematical structure of logic gate based on vector solitons [4, 9, 10]. Although there are many works about one-dimensional vector solitons, a mathematical work about two-dimensional vector solitons is still missing. For a more complete understanding mathematical structure of vector solitons, the study of two-dimensional vector solitons is very important. In this paper, we derive a two-component analogue of two-dimensional long wave-short wave resonance interaction (2c-2d-LSRI) equations in a physical setting. We also present the Wronskian solution of the integrable 2c-2d-LSRI equations.