应用Riccati展开法求解广义KdV-mKdV方程的新精确解
New Exact Solution for Generalized KdV-mKdV Equation via Riccati Expansion Method
摘要: 应用Riccati映射法，对广义KdV-mKdV方程进行新的精确解的研究，根据齐次平衡理论，得到了广义KdV-mKdV方程新的精确解，这些解包括双曲函数解和三角函数解。通过这些解中待求参数之间的关系，运用Maple软件得到了这些解的图象。此方法在求解其他非线性偏微分方程中也有重要的作用。
Abstract: The Riccati mapping method is used to study the new exact solutions of the generalized KdV-mKdV equation. According to the homogeneous equilibrium theory, the new exact solutions of the generalized KdV-mKdV equation are obtained, which include hyperbolic and trigonometric solutions. The images of these solutions are obtained by using Maple software. This method also plays an important role in solving other nonlinear partial differential equations.
文章引用：欧阳坦, 肖冰. 应用Riccati展开法求解广义KdV-mKdV方程的新精确解[J]. 理论数学, 2022, 12(1): 47-53. https://doi.org/10.12677/PM.2022.121007

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