The Pole Solution And Dynamic Property Analysis Of Continuous Nonlinear Schrodinger-type Equation

The nonlinear local wave phenomenon is a very concerned problem in the field of natural science,and the multipole solution,as a degenerate state of N-soliton solution,was first proposed by Zakharov and Shabat,and is now widely used in nonlinear optics and fluid mechanics,etc.This thesis is devoted to the study of the multi-pole(MP)solutions of nonlinear Schr(?)dinger(NLS)equation and Hirota equation and their dynamic properties.First,to solve this problem,N-soliton solutions are constructed based on the basic darboux transformation of NLS equation and Hirota equation,and then explicit expressions of arbitrary-order MP solutions of the two equations are obtained by using limit technique.Second,by an improved asymptotic analysis method relying on the balance between exponential and algebraic terms,the accurate expressions of all asymptotic solitons in the MP solutions of two equations.Finally,by analyzing the expression of asymptotic solitons,it is found that the asymptotic solitons distributed along the curve are separated from each other by logarithmic law before and after the interaction,and the interaction force decreases exponentially with the increase of distance,while the asymptotic solitons distributed along the line have constant velocity and no phase shift.In addition,this thesis also studies the near field regional interaction of the double-pole solutions of NLS equation and Hirota equation,and obtains the maximum and minimum values of the interaction of two pairs of solitons and the corresponding spatial and temporal positions under specific parameters by means of numerical calculation.