| 一类非线性双曲型发展方程的孤子解 |
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| 引用本文： | 冯依虎,陈贤峰,莫嘉琪.一类非线性双曲型发展方程的孤子解[J].应用数学和力学,2015,36(10):1076-1084. |
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| 作者姓名： | 冯依虎 陈贤峰 莫嘉琪 |
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| 作者单位： | 1亳州师范高等专科学校 电子与信息工程系, 安徽 亳州 236800;2上海交通大学 数学系, 上海 200240;3安徽师范大学 数学系, 安徽 芜湖 241003 |
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| 基金项目： | 国家自然科学基金(11371248)；安徽省教育厅自然科学课题(KJ2015A347;KJ2013B153) |
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| 摘 要： | 研究了一类非线性发展方程.首先在无扰动情形下，利用待定函数和泛函同伦映射方法得到了非扰动发展方程的孤子精确解和扰动方程的任意次近似行波孤子解.接着引入一个同伦映射，并选取初始近似函数,再用同伦映射理论,依次求出非线性双曲型发展扰动方程孤子解的各次近似解析解.再利用摄动理论举例说明了用该方法得到的近似解析解的有效性和各次近似解的近似度.最后,简述了用同伦映射方法得到的近似解的意义,指出了用上述方法得到的各次近似解具有便于求解、精度高等优点.
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| 关 键 词： | 孤子解 扰动 非线性双曲型方程 |
| 收稿时间： | 2015-05-25 |
The Soliton Solutions to a Class of Nonlinear Hyperbolic Evolution Equations |
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| Institution: | 1Department of Electronics and Information Engineering,Bozhou Teachers College, Bozhou, Anhui 236800, P.R.China;2Department of Mathematics, Shanghai Jiao Tong University,Shanghai 200240, P.R.China;3Department of Mathemtics, Anhui Normal University,Wuhu, Anhui 241003, P.R.China |
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| Abstract: | A class of nonlinear evolution equations were investigated. With the undetermined functions and functional homotopic mapping methods, the exact solitary solution to the non-disturbed evolution equation and the arbitrary order approximate travelling wave solitary solution to the disturbed evolution equation were obtained. A homotopic mapping was introduced, and an initial approximate function was chosen to find out successively the arbitrary order solitary approximate analytic solutions to the nonlinear hyperbolic evolution equation based on the homotopic mapping theory. With the perturbation method, the examples illustrated the validity and approximation degree of the arbitrary order approximate solutions. A discussion shows the practicability and high accuracy of the approximate solutions obtained with the proposed homotopic mapping method. |
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