基于(G'/G)展开法求解(1 + 1)维积分微分Ito方程的新精确解
New Exact Solution for (1 + 1)-Dimensional Integro-Differential Ito Equation Based on Expansion (G'/G) Method
摘要: (G'/G)展开法可以有效的求解出非线性偏微分方程的精确解。本文利用(G'/G)展开法及齐次平衡原则，对(1 + 1)维积分微分Ito方程进行求解，得到该方程新的精确解，这些解包括双曲函数解、三角函数解以及有理函数解。根据待定参数之间的关系对参数进行取值，运用数学软件Maple画出精确解的图像。
Abstract: The (G'/G) expansion method can effectively solve the exact solution of nonlinear partial differential equations. In this paper, we use the (G'/G) expansion method and the homogeneous balance rule to solve the (1 + 1) -dimensional integro-differential Ito equation, and obtain its new exact solutions, which include hyperbolic, trigonometric and rational solutions. According to the relationship between the undetermined parameters, the parameters are valued. The image of the exact solution is obtained by Maple software.
文章引用：邵廷朗, 翁琨锋. 基于(G'/G)展开法求解(1 + 1)维积分微分Ito方程的新精确解[J]. 应用数学进展, 2024, 13(7): 3140-3146. https://doi.org/10.12677/aam.2024.137299

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