非自治KP方程的周期抛物孤子
Periodic parabola solitons for the nonautonomous KP equation
摘要：
Kadomtsev-Petviashvili（KP）方程可以描述流体和等离子体中的不同模型，其孤立子解的研究方法很多。本文研究了（2+1）维非自治KP方程的周期抛物孤子，给出了方程参数的必要约束条件。利用Painleve分析和Hirota双线性方法，我们发现该解有六个待定参数，并分析了几种典型情形解的特征。在构造解的基础上，讨论了它们的收敛性条件。
英文摘要：
Kadomtsev-Petviashvili (KP) equation, who can describe different models in fluids and plasmas, has drawn investigation for its solitonic solutions with various methods. In this paper, we focus on the periodic parabola solitons for the (2+1) dimensional nonautonomous KP equations where the necessary constraints of the parameters are figured out. With Painleve analysis and Hirota bilinear method, we find that the solution has six undetermined parameters as well as analyze the features of some typical cases of the solutions. Based on the constructed solutions, the conditions of their convergence are also discussed.
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