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A (2+1)-dimensional breaking soliton equation: Solutions and conservation laws

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  • Yıldırım, Yakup
  • Yaşar, Emrullah

Abstract

In this paper, we consider a (2+1)-dimensional breaking soliton equation which describe the (2+1)-dimensional interaction of the Riemann wave propagating along the y-axis with a long wave along the x-axis. By the Lie group analysis, the Lie point symmetry generators and symmetry reductions were deduced. From the viewpoint of exact solutions, we have performed two distinct methods to the equation for getting some exact solutions. Kudryashov’s simplest methods and ansatz method with the assistance of Maple were carried out. The local conservation laws are also constructed by multiplier/homotopy methods. Finally, the graphical simulations of the exact solutions are depicted.

Suggested Citation

  • Yıldırım, Yakup & Yaşar, Emrullah, 2018. "A (2+1)-dimensional breaking soliton equation: Solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 146-155.
    • Handle: RePEc:eee:chsofr:v:107:y:2018:i:c:p:146-155
    DOI: 10.1016/j.chaos.2017.12.016
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    References listed on IDEAS

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    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Gandarias, M.L. & Rosa, M., 2016. "On double reductions from symmetries and conservation laws for a damped Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 560-565.
    3. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    4. Recio, E. & Gandarias, M.L. & Bruzón, M.S., 2016. "Symmetries and conservation laws for a sixth-order Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 572-577.
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