时空分数阶KdV-Burgers-Fisher方程的分数阶孤子解和新型波

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中图分类号：0175.2 文献标志码：A

doi： 10.3969/j .issn.1673-5862.2025.03.009

Some fractional soliton solutions and novel wave structures for the time-space-fractional KdV-Burgers-Fisher equations

YU Fajun ， KANG Qingqing （College of Mathematics and Systems Science， Shenyang Normal University，Shenyang 110o34，China）

Abstract： This paper conducts a study on fractional soliton solutions and their characteristics for the space-time fractional KdV-Burgers-Fisher equation with both time fractional α -orderderivative and space fractional β -order derivative. The hyperbolic tangent method is employed to solve the equation，and bright soliton，dark soliton，and kink soliton solutions are successfully obtained. The study reveals that when the time fractional order α is equal to the space fractional order β ，the corresponding solution graph exhibits a flat state; when the two orders are not equal，the solution graph shows a parabolic shape，and with the increase of the difference between α and β ，the degree of curvature of the parabola significantly enhances. In addition，special cases are analyzed，a fifthorder space-time fractional KdV-Burgers-Fisher equation is constructed， and the relevant characteristics of the two fractional solitons described by the equation are discussed. Through the above research，the influence law of the change in the order of fractional derivatives on the image characteristics of soliton solutions is revealed， providing a theoretical reference for the in-depth understanding of the dynamic behavior of solitons in space-time fractional nonlinear systems.

Key Words： time-space-fractional KdV-Burgers-Fisher equation； tanh method; bright soliton; dark soliton

KdV 方程是一个经典的非线性演化方程，是描述潜水波在自由表面上单向传播的可积潜水波模型[1]。（剩余6952字）