Degenerate and non-degenerate vector solitons and their interactions in the two-component long-wave–short-wave model of Newell type

Abstract

The focus of this paper is on the dynamics of degenerate and non-degenerate vector solitons and their collision scenarios in the two-component long-wave–short-wave (2-LS) model of Newell type. The model equation that we study here governs the resonance interactions between two capillary waves (short waves) with a common gravity wave (long wave) for the surface wave of deep water. These degenerate and non-degenerate soliton solutions of the 2-LS model of Newell type are constructed via the bilinear KP-hierarchy reduction method and are expressed in forms of determinants. The degenerate solitons having only single-hump or single-valley profiles can undergo both elastic and inelastic collisions. Two particular types of degenerate solitons are also obtained, i.e., bound state solitons and V/Y-shaped solitons. The non-degenerate solitons and their collision scenarios have more interesting properties in contrast with the degenerate ones. The obvious one is that the non-degenerate one solitons possess symmetric or asymmetric double-hump and double-valley profiles if they propagate with identical velocities in all short-wave (SW) and long-wave (LW) components. Additionally, the soliton wavenumbers in the SW components and the LW component are unequal if the ones in the two SW components propagate with different velocities. The non-degenerate two solitons can undergo two different types of elastic collision scenarios in both SW and LW components: shape-preserving and shape-changing scenarios. We also study the collisions of non-degenerate solitons with degenerate ones, and find some intriguing properties. For instance, if the degenerate one soliton in one of the two SW components vanishes into background, then there is only one fundamental non-degenerate soliton in the corresponding SW component. However, this fundamental non-degenerate soliton still alters its profile from a symmetric double-hump waveform to an asymmetric double-hump one during its propagation process without interacting with other solitons. Furthermore, it is found a new class of soliton solutions referred to as (1,2,3) solitons. In these new types of soliton solutions, one SW component has only a single soliton, the other SW component has two solitons, whereas the LW component has three solitons.