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On periodic wave solutions and asymptotic behaviors to a generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation

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Abstract.

In this paper, a lucid and systematic approach is proposed to systematically study the periodic-wave solutions and asymptotic behaviors of a (2 + 1) -dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. Based on Bell's polynomials, the bilinear formalism and N -soliton solution of the gKDKK equation are derived, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic-wave solutions of the equation are also constructed. Finally, an asymptotic relation between the periodic-wave solutions and soliton solutions are strictly established under a limited procedure.

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Authors and Affiliations

  1. Department of Mathematics, China University of Mining and Technology, 221116, Xuzhou, China

    Lian-Li Feng, Shou-Fu Tian, Hui Yan, Li Wang & Tian-Tian Zhang

  2. Center of Nonlinear Equations, China University of Mining and Technology, 221116, Xuzhou, China

    Lian-Li Feng, Shou-Fu Tian, Hui Yan & Tian-Tian Zhang

Authors
  1. Lian-Li Feng
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  2. Shou-Fu Tian
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  3. Hui Yan
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  4. Li Wang
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  5. Tian-Tian Zhang
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Correspondence to Shou-Fu Tian.

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Feng, LL., Tian, SF., Yan, H. et al. On periodic wave solutions and asymptotic behaviors to a generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation. Eur. Phys. J. Plus 131, 241 (2016). https://doi.org/10.1140/epjp/i2016-16241-1

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