A new general coupled (1+1) dimensional long wave short wave resonance interaction system: Derivation, bright solitons, and energy sharing collisions

A new solvable physical system describing nonlinear resonant interaction between two short waves and one long wave with four wave mixing (FWM) effect is derived from the three component general coupled Schrödinger system arising in nonlinear optics, by multiple scale perturbation method. Then by using the Hirota bilinearization method, bright multisoliton (say, N) solution of the general coupled long wave short wave resonance interaction system in one dimension is obtained in the Gram determinant form. The primary focus of this work is to observe the significant role of the FWM effect on the collisions between two bright solitons, three bright solitons, and the collision between a bound soliton and a standard soliton in the new general coupled (1+1) dimensional long wave short wave resonance interaction system. The system features two different energy sharing collisions in short wave components that can be inter switched by tuning the coefficient of four-wave mixing terms whereas solitons in the long wave component always undergo elastic collision accompanied by a phase shift. The presence of FWM enables the possibility of obtaining nonsingular solutions for a wider range of system parameters, for instance, even in the absence of self-phase modulation and cross-phase modulation effects. Three soliton dynamics and bound state soliton propagation are also explored.