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Conservation laws, exact solutions of time-space fractional generalized Ginzburg-Landau equation for shallow wake flows
Lei Fu,Huanhe Dong,C.M. Khalique,Hongwei Yang
Keywords:Shallow wake flows, time-space fractional generalized Ginzburg-Landau equation, conservation laws
Abstract:
      In this study, starting from the rigid-lid shallow water equations, an amplitude evolution equation is derived by using the multi-scale and perturbation analysis method. The resulting equation has complex coefficients and is called (2+1)-dimensional generalized Ginzburg-Landau(gGL) equation. Then, the (2+1)-dimensional time-space fractional gGL equation is obtained by using the semi-inverse method and fractional variational principle in the first time. Finally, the conservation laws and some exact solutions of the fractional gGL equation are discussed on the basis of Lie symmetry analysis and exp(?φ(ζ))-expansion method. By analyzing these solutions, we conclude that there are solitary waves and rogue waves in shallow wake flows.