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

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

doi: 10.3879/j.issn.1000-0887.2015.03.009
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
  • 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.
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