Bright, dark and breather soliton solutions of the generalized long-wave short-wave resonance interaction system

Abstract In this paper, we consider a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave (SW) and a long-wave (LW). The general N -bright and N -dark soliton solutions are derived using the Hirota bilinear method and they are written in a compact way using Gram determinants. Very interestingly, the fundamental bright soliton solution of the generalized LSRI system, in general, behaves like Korteweg-deVries (KdV) soliton. However, under a special condition, it also acts like the nonlinear Schro¨dinger (NLS) soliton. The fundamental dark-soliton solution admits anti-dark, grey, and complete black soliton profiles depending on the choice of wave parameters. The results of asymptotic analysis show that both bright and dark solitons undergo elastic collision with a finite phase shift. In addition to these, we demonstrate the existence of resonance interactions among the bright solitons by tuning the phase shift regime. Furthermore, we illustrate the various types of bright and dark soliton bound states. Also, we demonstrate the different types of profiles associated with the obtained breather solution.