Engui Fan 2009 J. Phys. A: Math. Theor. 42 095206 doi:10.1088/1751-8113/42/9/095206
Quasi-periodic waves and an asymptotic property for the asymmetrical Nizhnik–Novikov–Veselov equation
Engui Fan
Show affiliationsBased 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.
- PACS
- MSC
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35Q51 Solitons (See also 37K40)
35J60 Nonlinear PDE of elliptic type
37K40 Soliton theory, asymptotic behavior of solutions
- Subjects
- Dates
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Issue 9 (6 March 2009)
Received 1 October 2008, in final form 7 January 2009
Published 4 February 2009
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Quasi-periodic waves and an asymptotic property for the asymmetrical Nizhnik–Novikov–Veselov equation
Engui Fan 2009 J. Phys. A: Math. Theor. 42 095206
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