Dynamic Characteristics Of Solutions For Two Coupled Nonlinear Schr?dinger Equations

As one of the classical nonlinear evolution equations in the field of quantum mechanics,the nonlinear Schr?dinger equation is often used to describe the motion state of microscopic particles.With the development of science and technology and the complexity and diversity of natural phenomena,the single component nonlinear Schr?dinger equation can no longer well describe the law of particle motion,while the multi-component coupled nonlinear Schr?dinger equation can obtain more abundant analytical solutions and dynamic characteristics.In this article,the generalized Darboux transformation method is used to derive the high-order local wave solutions of two types of coupled nonlinear Schr?dinger equations.The interactions of dynamic characteristics of solitons,rogue waves and breathers are analyzed as follows,In the first chapter,the research background and significance of the three types of classical nonlinear local waves of solitons,rogue waves and breathers are introduced,and the research status of coupled nonlinear Schr?dinger equation is described in the world.The generalized Darboux transformation is described,and the main research work is summarized.In the second chapter,the dynamical properties of solitons,rogue waves and breather solutions of the three component coupled nonlinear Schr?dinger equation are studied.By using the generalized Darboux transformation,the seed solution related to the normalized distance and delay time is brought into the Lax pair equation,and the Nth-order localized wave solution is obtained.The interactions of the first-to the third-order localized waves are analyzed in detail.In the third chapter,the elastic collision,inelastic collision and bound states of high-order solitons in the three component coupled nonlinear Schr?dinger equation are studied.Based on the zero seed solution,the fundamental solution matrix is introduced into the Taylor expansion,and the expressions of the first-to fourth-order optical soliton solutions are obtained.Based on numerical simulation,the fourth-order soliton collisions are analyzed.In the fourth chapter,the dynamic behaviors of solitons colliding with each other in the two-component coherently coupled nonlinear Schr?dinger equation are researched.By classifying the real and imaginary parts of the spectral parameters,the collision behaviors between solitons are analyzed systematically,and the waveforms of the interaction between the second-order solitons are obtained.In the fifth chapter,the main work of this paper is summarized in detail,and the future research work is prospected.