A numerical study on the N-periodic wave solutions of two coupled bilinear equations

2021 ◽  
Author(s):  
Xue-Xia Wang ◽  
Jian-Qing Sun ◽  
Ying-Nan Zhang
Keyword(s):  
Numerical Study ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Bilinear Equations

scholarly journals EXACT ONE-PERIODIC AND TWO-PERIODIC WAVE SOLUTIONS TO HIROTA BILINEAR EQUATIONS IN (2+1) DIMENSIONS

2009 ◽  
Vol 24 (21) ◽  
pp. 1677-1688 ◽  
Author(s):  
WEN-XIU MA ◽  
RUGUANG ZHOU ◽  
LIANG GAO
Keyword(s):  
Theta Functions ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Riemann Matrix ◽  
Wave Solutions ◽  
Riemann Theta Functions ◽  
Bilinear Formulation ◽  
Propagation Of Waves ◽  
Hirota Bilinear ◽  
Bilinear Equations

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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