Darboux transformations for a matrix long-wave-short-wave equation and higher-order rational rogue-wave solutions

摘要

A new matrix long-wave-short-wave equation is proposed with the of help of the zero-curvature equation. Based on the gauge transformation between Lax pairs, both onefold and multifold classical Darboux transformations are constructed for the matrix long-wave-short-wave equation. Resorting to the classical Darboux transformation, a multifold generalized Darboux transformation of the matrix long-wave-short-wave equation is derived by utilizing the limit technique, from which rogue wave solutions, in particular, can be obtained by employing the generalized Darboux transformation. As applications, we obtain rogue-wave solutions of the long-wave-short-wave equation and some explicit solutions of the three-component long-wave-short-wave model, including soliton solutions, breather solutions, the first-order and higher-order rogue-wave solutions, and others by using the generalized Darboux transformation.