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Quasi-periodic wave solutions with asymptotic analysis to the Saweda-Kotera-Kadomtsev-Petviashvili equation

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Abstract

In this paper, the (2+1)-dimensional Saweda-Kotera-Kadomtsev-Petviashvili (SK-KP) equation is investigated, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. With the aid of generalized Bell’s polynomials, the Hirota’s bilinear equation and N-soliton solution are explicitly constructed to the SK-KP equation, respectively. Based on the Riemann theta function, a direct and lucid way is presented to explicitly construct quasi-periodic wave solutions for the SK-KP equation. The two-periodic waves admit two independent spatial periods in two independent horizontal directions, which are a direct generalization of one-periodic waves. Finally, the relationships between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure.

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Authors and Affiliations

  1. Department of Mathematics, China University of Mining and Technology, 221116, Xuzhou, People’s Republic of China

    Mei-Juan Xu, Shou-Fu Tian, Jian-Min Tu, Pan-Li Ma & Tian-Tian Zhang

  2. Center of Nonlinear Equations, China University of Mining and Technology, 221116, Xuzhou, People’s Republic of China

    Mei-Juan Xu, Shou-Fu Tian, Jian-Min Tu, Pan-Li Ma & Tian-Tian Zhang

Authors
  1. Mei-Juan Xu
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  2. Shou-Fu Tian
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  3. Jian-Min Tu
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  4. Pan-Li Ma
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  5. Tian-Tian Zhang
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Correspondence to Shou-Fu Tian or Tian-Tian Zhang.

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Xu, MJ., Tian, SF., Tu, JM. et al. Quasi-periodic wave solutions with asymptotic analysis to the Saweda-Kotera-Kadomtsev-Petviashvili equation. Eur. Phys. J. Plus 130, 174 (2015). https://doi.org/10.1140/epjp/i2015-15174-5

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