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Periodic wave solutions and asymptotic analysis of the Hirota–Satsuma shallow water wave equation
Author(s) -
Zhao Zhonglong,
Zhang Yufeng
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3362
Subject(s) - mathematics , riemann hypothesis , theta function , mathematical analysis , bilinear interpolation , partial differential equation , periodic wave , soliton , simple (philosophy) , waves and shallow water , nonlinear system , traveling wave , physics , philosophy , statistics , epistemology , quantum mechanics , thermodynamics
In this paper, we devise a simple way to explicitly construct the Riemann theta function periodic wave solution of the nonlinear partial differential equation. The resulting theory is applied to the Hirota–Satsuma shallow water wave equation. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function. We obtain the one‐periodic and two‐periodic wave solutions of the equation. The relations between the periodic wave solutions and soliton solutions are rigorously established. Copyright © 2014 John Wiley & Sons, Ltd.