Periodic wave solutions of coupled integrable dispersionless equations by residue harmonic balance

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• 作者：A.Y.T. Leung ; ^{bcaleung@cityu.edu.hk} ; H.X. Yang ; Z.J. Guo
• 关键词：Dispersionless ; Residue harmonic balance ; Nonlinear evolution equations ; Analytical approximation ; Periodic solution
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2012
• 出版时间：November, 2012
• 年：2012
• 卷：17
• 期：11
• 页码：4508-4514
• 全文大小：258 K

文摘

We introduce the residue harmonic balance method to generate periodic solutions for nonlinear evolution equations. A PDE is firstly transformed into an associated ODE by a wave transformation. The higher-order approximations to the angular frequency and periodic solution of the ODE are obtained analytically. To improve the accuracy of approximate solutions, the unbalanced residues appearing in harmonic balance procedure are iteratively considered by introducing an order parameter to keep track of the various orders of approximations and by solving linear equations. Finally, the periodic solutions of PDEs result. The proposed method has the advantage that the periodic solutions are represented by Fourier functions rather than the sophisticated implicit functions as appearing in most methods.