Quasiperiodic waves and asymptotic behavior for Bogoyavlenskii's breaking soliton equation in (2+1) dimensions

Details Quasiperiodic waves and asymptotic behavior for Bogoyavlenskii's breaking soliton equation in (2+1) dimensions Quasiperiodic waves and asymptotic behavior for Bogoyavlenskii's breaking soliton equation in (2+1) dimensions

Sep 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008phrve..78c6607f&link_type=abstract

Physical Review E, vol. 78, Issue 3, id. 036607

Statistics

Computation

17

Solitons, Computational Methods In Classical Mechanics, Mathematical Procedures And Computer Techniques

Scientific paper

Based on a multidimensional Riemann theta function, the Hirota bilinear method is extended to explicitly construct multiperiodic (quasiperiodic) wave solutions for the (2+1) -dimensional Bogoyavlenskii breaking soliton equation. 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 in shallow water. The two-periodic (biperiodic) waves are a direct generalization of one-periodic waves, their surface pattern is two dimensional, that is, they have two independent spatial periods in two independent horizontal directions. The two-periodic waves may be considered to represent periodic waves in shallow water without the assumption of one dimensionality. A limiting procedure is presented to analyze asymptotic behavior of the one- and two-periodic waves in details. The exact 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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