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Riemann theta functions periodic wave solutions and rational characteristics for the (1+1)-dimensional and (2+1)-dimensional Ito equation

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  • Tian, Shou-Fu
  • Zhang, Hong-Qing

Abstract

In this paper, based on a multidimensional Riemann theta function, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta functions periodic waves solutions for nonlinear differential equation such as the (1+1)-dimensional and (2+1)-dimensional Ito equations. Among these periodic waves, the one-periodic waves are well-known cnoidal waves, their surface pattern is one-dimensional, and often they are used as one-dimensional models of periodic waves. The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two dimensional that they have two independent spatial periods in two independent horizontal directions. A limiting procedure is presented to analyze asymptotic behavior of the multiperiodic periodic waves in details and the relations between the periodic wave solutions and soliton solutions are rigorously established.

Suggested Citation

  • Tian, Shou-Fu & Zhang, Hong-Qing, 2013. "Riemann theta functions periodic wave solutions and rational characteristics for the (1+1)-dimensional and (2+1)-dimensional Ito equation," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 27-41.
    • Handle: RePEc:eee:chsofr:v:47:y:2013:i:c:p:27-41
    DOI: 10.1016/j.chaos.2012.12.004
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    Cited by:

    1. Demiray, Seçil & Taşcan, Filiz, 2016. "Quasi-periodic solutions of (3+1) generalized BKP equation by using Riemann theta functions," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 131-141.
    2. Wang, Xiu-Bin & Tian, Shou-Fu & Xua, Mei-Juan & Zhang, Tian-Tian, 2016. "On integrability and quasi-periodic wave solutions to a (3+1)-dimensional generalized KdV-like model equation," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 216-233.

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