N-fold generalized Darboux transformation and soliton interactions for a three-wave resonant interaction system in a weakly nonlinear dispersive medium

In this paper, a three-wave resonant interaction system, which describes the resonant mixing of the waves in a weakly nonlinear dispersive medium, is studied. Starting from the first-order Darboux transformation, we construct an N-fold generalized Darboux transformation (GDT) in which n different spectral parameters are involved, where n and N are the positive integers, and n <= N. Utilizing the obtained N-fold GDT, we derive three types of the Y-shaped bright-dark-bright solitons. Those solitons have different characteristic lines as follows: three rays; one ray and two curves; one ray, one line and two curves. Interactions among the three kinds of Y-shaped bright-dark-bright solitons are graphically illustrated. Those interactions are shown to be elastic.

Automated summary

This paper studies the resonant mixing of waves in a weakly nonlinear dispersive medium. By constructing an N-fold generalized Darboux transformation, three types of Y-shaped bright-dark-bright solitons with different characteristic lines are obtained. Graphical illustrations show that the interactions among these solitons are elastic.