Stability Analysis Of Solitary Waves For Dual Power Nonlinear Schr?dinger Equations With Variable Coefficients

In this paper,we study the related problems of the solitary wave stability of the dual power nonlinear Schr?dinger equation(DPNLS)with variable coefficients,which could be applied in a Bose Einstein condensate(BECs)and nonlinear optics.Firstly,we obtain solitary wave solutions of DPNLS with variable coefficients by using similarity transformation.Secondly,using the perturbation method and the spectral theory,the Vakhitov-Kolokolov(VK)stability criterion of solitary wave solutions for DPNLS with variable coefficients is obtained.Then,by using the VK stability criterion,we study the stability of DPNLS with variable coefficients in different cases,mianly including nonautonomous DPNLS with harmonic potential,self-focusing nonlinearity,space-quadratic potential,cubic-quintic nonlinearity and non-karr nonlinearity so on.Finally,the numerical simulation method is also used to show the stability.