Solution and stability analysis of coupled nonlinear Schrodinger equations

We consider a new type of integrable coupled nonlinear Schrodinger (CNLS) equations proposed by our self [submitted to Phys. Plasmas (2011)]. The explicit form of soliton solutions are derived using the Hirota’s bilinear method. We show that the parameters in the CNLS equations only determine the regions for the existence of bright and dark soliton solutions. Finally, through the linear stability analysis, the modulational instability condition is given.