Exact One-Periodic and Two-Periodic Wave Solutions to Hirota Bilinear Equations in (2+1) Dimensions
Hirota bilinear equations, Riemann theta functions, one-periodic and two-periodic wave solutions
Digital Object Identifier (DOI)
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.
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Citation / Publisher Attribution
Modern Physics Letters A, v. 24, issue 21, p. 1677-1688
Scholar Commons Citation
Ma, Wen-Xiu; Zhou, Ruguang; and Gao, Liang, "Exact One-Periodic and Two-Periodic Wave Solutions to Hirota Bilinear Equations in (2+1) Dimensions" (2009). Mathematics and Statistics Faculty Publications. 134.