Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrodinger equations with focusing, defocusing and mixed type nonlinearities

摘要

Bright and bright-dark type multisoliton solutions of the integrableN-coupled nonlinear Schrodinger (CNLS) equations with focusing, defocusing andmixed type nonlinearities are obtained by using Hirota's bilinearization method.Particularly,for the bright soliton case, we present the Gram type determinantform of the n-soliton solution (n:arbitrary) for both focusing and mixed type non-linearities and explicitly prove that the determinant form indeed satisfies the cor-responding bilinear equations. Based on this, we also write down the multisolitonform for the mixed (bright-dark) type solitons. For the focusing and mixed typenonlinearities with vanishing boundary conditions the pure bright solitons exhibitdifferent kinds of nontrivial shape changing/energy sharing collisions character-ized by intensity redistribution, amplitude dependent phase-shift and change inrelative separation distances. Due to nonvanishing boundary conditions the mixedN-CNLS system can admit coupled bright-dark solitons. Here we show that thebright solitons exhibit nontrivial energy sharing collision only if they are spreadup in two or more components, while the dark solitons appearing in the remain-ing components undergo mere standard elastic collisions. Energy sharing collisionslead to exciting applications such as collision based optical computing and solitonamplification. Finally, we briefly discuss the energy sharing collision properties ofthe solitons of the (2 + 1) dimensional long wave-short wave resonance interaction(LSRI) system.