适形分数阶导数下的分数阶KdV方程的多孤子解

"Multi-soliton Solutions of the Fractional KdV Equation Under Conformable Fractional Derivative"

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中图分类号：0193；0175.2 文献标识码：A 文章编号：1674-0033(2025)06-0017-05

Multi-soliton Solutions of the Fractional KdV Equation Under Conformable Fractional Derivative

HE Wei-jun, JIANG Ling-feng

(School of Mathematics and Computer Science, Chongqing College of International Business and Economics, Hechuan 401520,chongqing)

Abstract:Inorder to obtain the multi-soliton solutions of the conformable fractional KdV equation,with thehelp of the special property of conformable fractional derivative,the multi-soliton problem of the fractional KdV equation can be transformed into the multi-soliton problem of the integer order KdV equation through a special variable transformation,and then the multi-soliton is obtained through the method of bilinear derivative.Expressions for the 1-soliton solution and 2- solitonsolution of the conformable fractional KdV equation as well as a recursive formula for the arbitrary n-soliton solution are obtained.Compared with the traditional method,this method reduces the complexity of the solution process to a certain extent,and this method has some generalityand can be applied to the solution processof other soliton equations.

Key Words:conformable fractional derivative; fractional KdV equation;soliton solutior

分数阶导数的概念1首次于1695年被提出，但到目前为止，分数阶导数尚未像整数阶导数那样形成统一的定义。（剩余14764字）