Elastic Two-Kink, Breather, Multiple Periodic, Hybrid and Half-/Local-Periodic Kink Solutions of a Sharma-Tasso-Olver-Burgers Equation for the Nonlinear Dispersive Waves

• Tian-Yu Zhou ^[1] ; Bo Tian ^[1] ; Yu-Qi Chen ^[1]
  1. [1] Beijing University of Posts and Telecommunications

     Beijing University of Posts and Telecommunications

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Burgers-type equations are used to describe certain phenomena in plasma astrophysics, ocean dynamics, atmospheric science and so on. In this paper, a Sharma-Tasso-OlverBurgers equation for the nonlinear dispersive waves is studied. Based on the Cole-Hopf transformation and a bilinear form, elastic-two-kink solutions are worked out, which can describe the elastic interaction between the two kink waves. Some complex conjugated transformations are obtained for us to construct the corresponding breather solutions. Via the breather solutions, multiple periodic solutions are derived. According to symbolic computation, hybrid solutions composed of the kink waves and breathers as well as half-/local-periodic kink solutions are seen. Moreover, the above solutions are graphically depicted for us to understand the influence of the coefficients and interaction of the waves: velocities and periods of all the aforementioned waves rely on the coefficients; except the breathers and one of the kink waves of the elastic-two-kink solutions, the waves are independent of the coefficients.

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