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Group-invariant solutions, non-group-invariant solutions and conservation laws of Qiao equation |
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| Authors: | Jianping Shi Mengmeng Zhou and Hui Fang |
| Institution: | Department of System Science and Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, P.R. China,Department of System Science and Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, P.R. China and Department of System Science and Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, P.R. China |
| Abstract: | 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. |
| Keywords: | Qiao equation group-invariant solution non-group-invariant solution traveling wave-like solution variable amplitude variable velocity conservation law |
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