Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 42, Issue 9, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/42/9/095206
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Funding
- Department of Mathematics of the University of Missouri, USA
- National Key Basic Research Project of China [2004CB318000]
- Shanghai Shuguang Tracking Project [08GG01]
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Based on a multi-dimensional Riemann theta function, the Hirota bilinear method is extended to explicitly construct multi-periodic (quasi-periodic) wave solutions for the asymmetrical Nizhnik-Novikov-Veselov equation. Among these periodic waves, two-periodic waves are a direct generalization of well-known cnoidal waves; their surface pattern is two dimensional. The main physical result is the description of the behavior of nonlinear waves in shallow water. A limiting procedure is presented to analyze asymptotic properties of the two-periodic waves in details. Relations between the periodic wave solutions and the well-known soliton solutions are established. It is rigorously shown that the periodic wave solutions tend to the soliton solutions under a 'small amplitude' limit.
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