Lie symmetry analysis, bifurcations and exact solutions for the (2+1)-dimensional dissipative long wave system

Abstract

By the combination of Lie symmetry analysis and dynamical system method, the (2+1)-dimensional dissipative long wave system is studied. First, we get Lie algebra and Lie symmetry group of the system. Then, by using the dynamical system method, the bifurcation and phase portraits of the corresponding traveling system of the system are obtained, it is shown that for different parametric space, the system has infinitely many solitary wave solutions, periodic wave solutions, kink or anti kink wave solutions. At last, the conservation laws of the system are given.

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Acknowledgements

The authors would like to thank the Editor an Reviewers for their valuable comments.

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Correspondence to Hanze Liu.

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This work was supported by the National Natural Science Foundation of China under Grant Nos. 11171041 and 11505090, the high-level personnel foundation of Liaocheng University under Grant Nos. 31805 and 318011613.

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Chang, L., Liu, H. & Xin, X. Lie symmetry analysis, bifurcations and exact solutions for the (2+1)-dimensional dissipative long wave system. J. Appl. Math. Comput. (2020). https://doi.org/10.1007/s12190-020-01381-0

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Keywords

  • (2+1)-dimensional dissipative long wave system
  • Lie symmetry analysis
  • Bifurcation
  • Traveling wave solution
  • Conservation law

Mathematics Subject Classification

  • 37K10
  • 35C05