摘要
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.
基金
supported by the Natural Science Foundation of Guangdong Province of China(No.2021A1515012214)
the Science and Technology Program of Guangzhou(No.2019050001)
National Natural Science Foundation of China(Nos.12175111)
K C Wong Magna Fund in Ningbo University。
