This paper deals with the double power nonlinear Schrodinger equation in one dimension, which is proposed as a model to describe the Bose-Einstein condensate with mixed state interactions. The equation admits unstable solitons in the L 2 supercritical case. In terms of Cote , Martel and Merle’s argument, multi solitons of the equation are constructed by using unstable solitons in the L 2 supercritical case, which extend Cote , Martel and Merle’s results from the pure power case to the double power nonlinear cases.

This paper studies the inhomogeneous nonlinear Schrödinger equations, which may model the propagation of laser beams in nonlinear optics. Using the cross-constrained variational method, a sharp condition for global existence is derived. Then, by solving a variational problem, the strong instability of solitary waves of this equation is proved.