EXACT ONE-PERIODIC AND TWO-PERIODIC WAVE SOLUTIONS TO HIROTA BILINEAR EQUATIONS IN (2+1) DIMENSIONS
By Wenxiu Ma, Ruguang Zhou, Liang Gao. 2008
174 citations recorded by the source corpus.
Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitrary purely imaginary Riemann matrix. The resulting theory is applied to two nonlinear equations possessing Hirota bilinear forms: ut + uxxy - 3uuy - 3uxv = 0 and ut + uxxxxy - (5uxxv + 10uxyu - 15u2v)x = 0 where vx = uy, thereby yielding their one-periodic and two-periodic wave solutions describing one-dimensional propagation of waves.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/80ba355a4bf751fad3e8f2c3e20beace18dd1ad9
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In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation (2012, methodology): “Another example, by means of the Hirota bilinear method, Nakamura, Fan, and one of the authors have obtained periodic wave solutions in terms of Riemann theta function of several NLEEs [5, 15–18].”
- A multiple exp-function method for nonlinear differential equations and its application (2010, background): “It is known that there are multiple wave solutions to nonlinear equations, for instance, multi-soliton solutions to many physically significant equations including the KdV equation and the Toda lattice equation [18] and multiple periodic wave solutions to Hirota bilinear equations [19, 20].”