Based on the Hirota's method,the multiple-pole solutions of the focusing Schr?dinger equation are derived directly by introducing some new ingenious limit methods.We have carefully investigated these multi-pole solutions from three perspectives:rigorous mathematical expressions,vivid images,and asymptotic behavior.Moreover,there are two kinds of interactions between multiple-pole solutions:when two multiple-pole solutions have different velocities,they will collide for a short time;when two multiple-pole solutions have very close velocities,a long time coupling will occur.The last important point is that this method of obtaining multiple-pole solutions can also be used to derive the degeneration of N-breather solutions.The method mentioned in this paper can be extended to the derivative Schr?dinger equation,Sine-Gorden equation,mKdV equation and so on.

Zhao Zhang;Junchao Chen;Qi Guo

Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices,South China Normal University,Guangzhou 510631,China;Department of Mathematics and Institute of Nonlinear Analysis,Lishui University,Lishui 323000,China

理论物理

[1]Zhao Zhang;Junchao Chen;Qi Guo-.Multiple-pole solutions and degeneration of breather solutions to the focusing nonlinear Schr?dinger equation)[J].理论物理,2022(04):13-22

Gorden

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