General two-component long-wave short-wave resonance interaction system: Non-degenerate vector solitons and their collision dynamics

In this paper, we demonstrate the emergence of non-degenerate bright solitons and summarize their several interesting features in a completely integrable two-component long-wave–short-wave resonance interaction (LSRI) model with a general form of nonlinearity coefficients. This model describes the nonlinear resonant interaction between a low-frequency long wave and two high-frequency short waves in a one-dimensional physical setting. Through the classical Hirota’s bilinear method, we obtain a fully non-degenerate N-soliton solution in Gram determinant form for this two-component LSRI model to analyze the nature of non-degenerate vector solitons in detail. Depending on the choice of velocity conditions, the obtained non-degenerate fundamental soliton is classified into two types, namely (1,1,1)- and (1,1,2)-non-degenerate one solitons. We then show that the basic (1,1,1)-non-degenerate soliton exhibits five distinct profile structures, including a novel double-hump, a special flat-top, and a conventional single-hump profile, and (1,1,2)-non-degenerate soliton admits two-soliton like oblique collision, a behavior akin to KP line soliton interaction with a short stem structure. A detailed asymptotic analysis is carried out to study the long time behavior of (1,1,1)-non-degenerate solitons and it reveals that they undergo both shape-preserving and shape-changing collisions. However, our analysis confirms that the shape changing collision between these solitons become elastic in nature after appropriate shift of time coordinates. Further, we identified that the (1,1,2)-non-degenerate solitons also undergo elastic collision. In addition, we have also investigated the formation or suppression of breathing phenomena during collision between a degenerate soliton and a (1,1,1)-non-degenerate soliton by considering partially non-degenerate multi-soliton solution. For completeness, we also point out the collision scenario between the completely degenerate solitons. The results presented in this paper are broadly applicable to Bose–Einstein condensates, nonlinear optics, plasma physics, and other closely related fields where the LSRI phenomenon plays a significant role in governing the evolution of vector solitons.