Periodic wave solutions of coupled integrable dispersionless equations by residue harmonic balance |
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| Authors: | AYT Leung HX Yang ZJ Guo |
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| Institution: | 1. School of Engineering, Western Sydney University, Locked Bag 1797, Penrith, NSW, 2751, Australia;2. Institute of Geotechnical Engineering, School of Civil Engineering and Architecture, East China Jiao Tong University, Nanchang, 330013, Jiangxi, PR China;3. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China;4. School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China;5. Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, PR China |
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| Abstract: | 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. |
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