Chirped solutions and dynamical properties of the resonant Schr?dinger equation with quadratic-cubic nonlinearity  

作　　者：TANG Jia-xuan 

机构地区：[1]Department of Mathematics,Northeast Petroleum University,Daqing 163318,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2025年第1期223-237,共15页高校应用数学学报(英文版)(B辑)

摘　　要：In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.

关 键 词：chirped solutions bifurcation theory trial equation method quadratic-cubic nonlinearity non-linear waves 

分 类 号：O17[理学—数学]