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

Shou-Fu Tian and Hong-Qing Zhang

Chaos, Solitons & Fractals, 2013, vol. 47, issue C, 27-41

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.

Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:47:y:2013:i:c:p:27-41

DOI: 10.1016/j.chaos.2012.12.004

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