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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.