一类新的KdV方程的周期解
A New Class of Periodic Solutions to the KdV Equation
DOI: 10.12677/aam.2025.145229, PDF,    科研立项经费支持
作者: 李盼林, 包芳臣, 张静漪, 张 宁*：新疆农业大学数理学院，新疆 乌鲁木齐
关键词: KdV方程；Hirota双线性形式；周期解；孤波解；KdV Equation； Hirota Bilinear Form； Periodic Solutions； Solitary-Wave Solutions
摘要: 本文根据三波法的思想，结合一类新的KdV方程的Hirota双线性形式，通过选择特定形式的试探函数，构造出该方程的孤波解与周期解，并对解中的参数赋值，利用计算机符号软件对部分解进行了数值模拟，观察解的三维波形图与动力学演化过程。
Abstract: In this paper, based on the idea of the three-wave method, combined with a new class of Hirota bilinear forms of the KdV equation, we constructed the solitary-wave solution and the periodic solution of the equation by choosing a specific form of the trial function and assigning values to the parameters in the solution, and numerically simulated some of the solutions by using the computer symbolic software, observing the three-dimensional waveform plots of the solutions with the dynamics evolution process.
文章引用：李盼林, 包芳臣, 张静漪, 张宁. 一类新的KdV方程的周期解[J]. 应用数学进展, 2025, 14(5): 23-28. https://doi.org/10.12677/aam.2025.145229

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