Exact periodic steady solutions for nonlinear wave equations: A new approach |
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| Institution: | 1. Department of Mathematics and Statistics, Monash University, Clayton, Melbourne, Vict. 3168, Australia;2. City University of Hong Kong, Hong Kong, China;1. Department of Mathematics, Dongguk University, Seoul 04620, Republic of Korea;2. School of Mathematics & Computing (Mathematics), Yonsei University, Seoul 03722, Republic of Korea;3. Department of Mathematics, Chung-Ang University, Seoul 06974, Republic of Korea |
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| Abstract: | In many practical physical problems, the nonlinear wave equations of interest are nonintegrable. In some cases they may be close to an integrable equation, and in this case perturbation techniques are available. However, even in these cases and certainly in general, it is useful to construct exact explicit solutions. Here we introduce a new method for finding exact and explicit periodic travelling wave solutions, from which solitary wave solutions can be extracted if they exist. |
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