期刊
CHAOS SOLITONS & FRACTALS
卷 47, 期 -, 页码 27-41出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2012.12.004
关键词
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资金
- Doctoral Academic Freshman Award of Ministry of Education of China
- Natural Sciences Foundation of China [50909017]
- Mathematics +X Key Project of Dalian University of Technology
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. (C) 2012 Elsevier Ltd. All rights reserved.
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