适形分数阶导数下的2+1维KP方程的半域孤子解  

Semi-Domain Soliton Solution of the (2+1)-Dimensional KP Equation under the Conformable Fractional Derivative

作　　者：何伟军 吴春 HE Weijun;WU Chun(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2023年第6期65-71,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11361023);重庆市自然科学基金面上项目(No.cstc2019jcyj-msxmX0390);重庆市教育科学规划课题《现代信息技术与高校数学教学深度融合实践研究》(No.K22YG205144)。

摘　　要：为了研究适形分数阶导数定义下分数阶孤子方程的多孤子解,利用分数阶复变换法将分数阶孤子方程变换为整数阶孤子方程,然后用传统的双线性法求分数阶孤子方程的多孤子解。得到了分数阶Kadomtsev-Petviashvili(KP)方程的1-孤子解、2-孤子解的显式表达式以及任意n-孤子解的递推公式,比较了整数阶孤子和相应的分数阶孤子,讨论了2-孤子在传播过程中2个孤子的相互作用。通过对比发现,适形分数阶导数定义下的分数阶KP方程的孤子解与整数阶导数定义下的KP方程的孤子解在动力学行为上存在一些差异。To study the multi-soliton solutions of the fractional order soliton equation under the definition of conformable fractional derivatives.By using the fractional order complex transformation method,the fractional order soliton equation is transformed into an integer order soliton equation,and then solved by the traditional bilinear method to obtain the multi-soliton solution of the fractional order soliton equation.The 1-soliton solution,the explicit expression of the 2-soliton solution,and the recursive formula of the arbitrary n-soliton solution of the fractional KP equation are obtained,the integer-order soliton and the corresponding fractional-order soliton are compared,and the interaction of the two solitons in the propagation process of 2-soliton is discussed.Through comparison,it is found that there are some differences in dynamic behavior between the soliton solution of the fractional KP equation defined by the conformable fractional derivative and the soliton solution of the KP equation defined by the integer order derivative.

关 键 词：适形分数阶导数 非线性分数阶偏微分方程 分数阶2+1维KP方程 半域孤子解 

分 类 号：O193[理学—数学] O175.2[理学—基础数学]