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

FENG Yi-hu; SHI Lan-fang; WANG Wei-gang; MO Jia-qi

doi:10.3879/j.issn.1000-0887.2015.03.009

Volume 36 Issue 3

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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

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

doi: 10.3879/j.issn.1000-0887.2015.03.009

¹Department of Science and Technology, Bozhou Teachers College, Bozhou, Anhui 236800, P.R.China;²College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, P.R.China;³Tongcheng Teaching Department, Anqing Normal University, Tongcheng, Anhui 231402, P.R.China;⁴Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(11202106)

Received Date: 2014-11-19
Rev Recd Date: 2014-12-11
Publish Date: 2015-03-15

Abstract

Abstract

A class of generalized nonlinear strong-damp disturbed evolution differential equations were studied, which widely appeared in the fields of mathematics, mechanics and physics etc.. Firstly, a travelling wave transformation was introduced to convert the related problem of partial differential equations to one of travelling wave equations, with the exact solution to the original typical problem obtained. Then the small parameter method was used and the stretched variables introduced to construct the asymptotic solution. Finally, the existence, high accuracy and uniform validity of the asymptotic travelling wave solution to the original generalized nonlinear strong-damp disturbed evolution equation for the initial-value problem were proved with the fixed point theory for functional analysis. The presented travelling wave asymptotic solution is an analytic expansion, therefore, it is continuously open to analytic operations, which reject the solutions given by those pure numerical methods.
- travelling wave,
- strong damp,
- evolution equation

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References(21)

References

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