On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation

Abstract

A vector modified Yajima−Oikawa long-wave−short-wave equation is proposed using the zero-curvature presentation. On the basis of the Riccati equations associated with the Lax pair, a method is developed to construct multi-fold classical and generalized Darboux transformations for the vector modified Yajima−Oikawa long-wave−short-wave equation. As applications of the multi-fold classical Darboux transformations and generalized Darboux transformations, various exact solutions for the vector modified long-wave−short-wave equation are obtained, including soliton, breather, and rogue wave solutions.

Keywords

• vector modified long-wave–short-wave equation
• multi-fold generalized darboux transformation
• soliton solutions
• breather solutions
• rogue wave solutions