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一类广义非线性强阻尼扰动发展方程的行波解

冯依虎 石兰芳 汪维刚 莫嘉琪

冯依虎, 石兰芳, 汪维刚, 莫嘉琪. 一类广义非线性强阻尼扰动发展方程的行波解[J]. 应用数学和力学, 2015, 36(3): 315-324. doi: 10.3879/j.issn.1000-0887.2015.03.009
引用本文: 冯依虎, 石兰芳, 汪维刚, 莫嘉琪. 一类广义非线性强阻尼扰动发展方程的行波解[J]. 应用数学和力学, 2015, 36(3): 315-324. doi: 10.3879/j.issn.1000-0887.2015.03.009
FENG Yi-hu, SHI Lan-fang, WANG Wei-gang, MO Jia-qi. Travelling Wave Solution to a Class of Generalized Nonlinear Strong-Damp Disturbed Evolution Equations[J]. Applied Mathematics and Mechanics, 2015, 36(3): 315-324. doi: 10.3879/j.issn.1000-0887.2015.03.009
Citation: FENG Yi-hu, SHI Lan-fang, WANG Wei-gang, MO Jia-qi. Travelling Wave Solution to a Class of Generalized Nonlinear Strong-Damp Disturbed Evolution Equations[J]. Applied Mathematics and Mechanics, 2015, 36(3): 315-324. doi: 10.3879/j.issn.1000-0887.2015.03.009

一类广义非线性强阻尼扰动发展方程的行波解

doi: 10.3879/j.issn.1000-0887.2015.03.009
基金项目: 国家自然科学基金(11202106)
详细信息
    作者简介:

    冯依虎(1982—),男,安徽潜山人,讲师,硕士(E-mail: fengyihubzsz@163.com);莫嘉琪(1937—),男,浙江德清人,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

  • 中图分类号: O175.29

Travelling Wave Solution to a Class of Generalized Nonlinear Strong-Damp Disturbed Evolution Equations

Funds: The National Natural Science Foundation of China(11202106)
  • 摘要: 研究了一类非线性强阻尼广义扰动发展方程问题.它们在数学、力学、物理学等领域中广泛出现.首先,引入一个行波变换,把相应的偏微分方程问题转化为行波方程问题并求出原典型问题的精确解.再用小参数方法和引入伸长变量构造了问题的渐近解.最后, 用泛函分析的不动点理论证明了原非线性强阻尼广义扰动发展方程初值问题渐近行波解的存在性,并证明渐近解具有较高的精度和一致有效性.该文求得的渐近解是一个解析展开式, 所以它还可继续进行解析运算, 而单纯用数值模拟的方法是不行的.
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出版历程
  • 收稿日期:  2014-11-19
  • 修回日期:  2014-12-11
  • 刊出日期:  2015-03-15

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