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Volume 9, Number 5, 2019, Pages 2023-2036                                                                DOI:10.11948/20190110
Group-invariant solutions, non-group-invariant solutions and conservation laws of Qiao equation
Jianping Shi,Mengmeng Zhou,Hui Fang
Keywords:Qiao equation, group-invariant solution, non-group-invariant solution, traveling wave-like solution, variable amplitude, variable velocity, conservation law.
      This paper considers a completely integrable nonlinear wave equation which is called Qiao equation. The equation is reduced via Lie symmetry analysis. Two classes of new exact group-invariant solutions are obtained by solving the reduced equations. Specially, a novel technique is proposed for constructing group-invariant solutions and non-group-invariant solutions based on travelling wave solutions. The obtained exact solutions include a set of traveling wave-like solutions with variable amplitude, variable velocity or both. Nonlocal conservation laws of Qiao equation are also obtained with the corresponding infinitesimal generators.
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