| Fisher方程的有界衰减振荡解 |
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| 引用本文： | 李向正.Fisher方程的有界衰减振荡解[J].物理学报,2012,61(17):170507-170507. |
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| 作者姓名： | 李向正 |
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| 作者单位： | 河南科技大学数学与统计学院,洛阳,471003 |
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| 基金项目： | 国家自然科学基金(批准号: 10871129);河南省教育厅自然科学基金项目(批准号: 2011B110013)和河南科技大学科研创新能力培育基金项目(2010CZ0016)资助的课题. |
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| 摘 要： | 为了研究非线性发展方程的有界衰减振荡解,特选取Fisher方程为例. Fisher方程在描述激发介质的非数值模型(如Belousov-Zhabotinsky (BZ)反应)中, 其解的振幅取负值是有意义的.应用平面动力系统理论,研究了Fisher方程有界行波解存在的条件, 利用LS解法和线性化解法给出了其有界衰减振荡解的近似解析表达式,并进行了误差估计.
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| 关 键 词： | Fisher方程 平面动力系统 衰减振荡解 误差估计 |
| 收稿时间： | 2012-01-02 |
Bounded damped oscillatory solutions of Fisher equation |
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| Li Xiang-Zheng.Bounded damped oscillatory solutions of Fisher equation[J].Acta Physica Sinica,2012,61(17):170507-170507. |
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| Authors: | Li Xiang-Zheng |
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| Institution: | College of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China |
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| Abstract: | To research the bounded damped oscillatory solutions of nonlinear evolution equation, we choose the Fisher equation as an example. The solutions with negative amplitudes of Fisher equation may become meaningful in the context of nonscalar models describing excitable media (e.g. the Belousov-Zhabotinsky (BZ) reaction). The theory of planar dynamical systems is used to study the existence conditions of bounded traveling wave solutions of Fisher equation. The bounded approximate damped oscillatory analytic solution is given by using LS method and linearization method. And its error is also estimated. |
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| Keywords: | Fisher equation planar dynamic system damped oscillatory solutions error estimate |
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