THEORETICAL STUDY OF ONE-DIMENSIONAL QUANTUM SYSTEM WITH GENERALIZED CUBIC-QUINTIC NONLINEARITY

We study the (1+1)-dimensional nonlinear Schr¨odinger equation with double nonlinear terms that are in the form of polytropic approximation and generalized from cubic-quintic formulation. We find the analytical solution of such equation model by the F-expansion method without introducing any integrability constraint. Based on the derived dark soliton solution, we calculate the polytropic index dependence of the soliton velocity and soliton ampitude and show the simulated dark soliton evolutionary variation because of different nonlinear strength, giving quantitative evaluation of the dynamical behavior variation of the typical (1+1)-dimensional quantum system that depends on the parameterized generalized cubic-quintic nonlinearity.