| 非线性扰动广义NNV系统的孤立子渐近行波解 |
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| 引用本文： | 史娟荣,吴钦宽,莫嘉琪. 非线性扰动广义NNV系统的孤立子渐近行波解[J]. 应用数学和力学, 2015, 36(9): 1003-1010. DOI: 10.3879/j.issn.1000-0887.2015.09.011 |
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| 作者姓名： | 史娟荣 吴钦宽 莫嘉琪 |
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| 作者单位： | 1安徽机电职业技术学院, 安徽 芜湖 241002;2南京工程学院 数理系, 南京 211167;3安徽师范大学 数学系, 安徽 芜湖 241003;4上海交通大学 数学系,上海 200240 |
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| 基金项目： | 国家自然科学基金(11202106) |
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| 摘 要： | 采用了一个简单而有效的技巧，研究一类非线性扰动广义NNV(Nizhnik-Novikov-Veselov)系统.首先用待定系数法得到一个相应典型系统的孤立子解.其次构造一个广义泛函式，并对它进行变分计算,利用变分原理求出对应的Lagrange乘子,并由此构造一个特殊的变分迭代关系式.然后依次求出原非线性扰动广义NNV系统的孤立子渐近行波解.最后通过举例,说明了使用该方法得到的近似解具有简单而有效的优点.
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| 关 键 词： | 孤立子 扰动NNV系统 迭代方法 |
| 收稿时间： | 2015-03-05 |
Asymptotic Travelling Wave Soliton Solutions for Nonlinear Disturbed Generalized NNV Systems |
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| Affiliation: | 1Anhui Technical College of Mechanical and Electrical Engineering,Wuhu, Anhui 241002, P.R.China;2Department of Mathematics & Physics, Nanjing Institute of Technology, Nanjing 211167, P.R.China;3Department of Mathematics, Anhui Normal University,Wuhu, Anhui 241003, P.R.China;4Department of Mathematics, Shanghai Jiao Tong University,Shanghai 200240, P.R.China |
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| Abstract: | A class of nonlinear disturbed generalized NNV (Nizhnik Novikov Veselov) system was addressed with a simple and valid technique. Firstly, the soliton solution to the corresponding typical differential system was obtained by means of the undetermined coefficient method. Secondly, a generalized functional equation was built and variationally calculated, and the corresponding Lagrange multiplier was derived according to the variation principle. Thereby, a special variational iteration relation expression was constructed. Then, the asymptotic travelling wave soliton solution for the original nonlinear disturbed generalized NNV system was attained successively. Finally, through an example, the proposed approximate analysis method is proved to be convenient and effective. |
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