ZHANG Li-jun, CHEN Li-qun. Sub-Equations and Exact Traveling Wave Solutions to a Class of High-Order Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2015, 36(5): 548-554. doi: 10.3879/j.issn.1000-0887.2015.05.010
Citation:
ZHANG Li-jun, CHEN Li-qun. Sub-Equations and Exact Traveling Wave Solutions to a Class of High-Order Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2015, 36(5): 548-554. doi: 10.3879/j.issn.1000-0887.2015.05.010
ZHANG Li-jun, CHEN Li-qun. Sub-Equations and Exact Traveling Wave Solutions to a Class of High-Order Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2015, 36(5): 548-554. doi: 10.3879/j.issn.1000-0887.2015.05.010
Citation:
ZHANG Li-jun, CHEN Li-qun. Sub-Equations and Exact Traveling Wave Solutions to a Class of High-Order Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2015, 36(5): 548-554. doi: 10.3879/j.issn.1000-0887.2015.05.010
1School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, P.R.China;2International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, NorthWest University, Mafikeng Campus, Mmabatho 2735, South Africa;3Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China
Funds:
The National Natural Science Foundation of China(11101371)
The exact traveling wave solutions to a class of 5th-order nonlinear wave equations were studied with the sub-equation method and the dynamic system analysis approach. The lower-order sub-equations of this class of high-order nonlinear equations were first derived, then the traveling wave solutions were investigated via the various exact solutions to the sub-equations under different parameter conditions. As an example, 2 families of exact valley-form solitary wave solutions and 2 families of smooth periodic traveling wave solutions to the Sawada-Kotera equation were presented. This method can be applied to study the traveling wave solutions to high-order nonlinear wave equations of which the corresponding traveling wave system can be reduced to the nonlinear ODEs involving only even-order derivatives, sum of squares of 1st-order derivatives and polynomial of dependent variables.
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