Bright-dark mixed $N$-soliton solutions of the multi-component Mel'nikov system

Abstract

By virtue of the KP hierarchy reduction technique, we construct the general bright-dark mixed $N$-soliton solution to the multi-component Mel'nikov system comprised of multiple (say $M$) short-wave components and one long-wave component with all possible combinations of nonlinearities including all-positive, all-negative and mixed types. Firstly, the two-bright-one-dark (2-b-1-d) and one-bright-two-dark (1-b-2-d) mixed $N$-soliton solutions in short-wave components of the three-component Mel'nikov system are derived in detail. Then we extend our analysis to the $M$-component Mel'nikov system to obtain its general mixed $N$-soliton solution. The formula obtained unifies the all-bright, all-dark and bright-dark mixed $N$-soliton solutions. For the collision of two solitons, the asymptotic analysis shows that for a $M$-component Mel'nikov system with $M\ge 3$, inelastic collision takes place, resulting in energy exchange among the short-wave components supporting bright solitons only if the bright solitons appear at least in two short-wave components. Whereas, the dark solitons in the short-wave components and the bright solitons in the long-wave component always undergo elastic collision which just accompanied by a position shift.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1706.05498

References in corpus (8)

• Theory of Bose-Einstein condensation in trapped gases
• General high-order rogue waves and their dynamics in the nonlinear Schroedinger equation
• Rogue waves in the Davey-Stewartson equation
• Dynamics of rogue waves in the Davey-Stewartson II equation
• Multicomponent long-wave--short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons
• General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions
• General Mixed Multi-Soliton Solutions to One-Dimensional Multicomponent Yajima-Oikawa System
• Multi-dark soliton solutions of the two-dimensional multi-component Yajima-Oikawa systems

Cited by in corpus (2)

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