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On the periodic solutions for both nonlinear differential and difference equations: A unified approach |
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| Authors: | Engui Fan Kwok Wing Chow |
| Institution: | a School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai, 200433, PR China b Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong |
| Abstract: | A direct and unifying scheme for disclosure of periodic wave solutions of both nonlinear differential and difference equations is presented. The scheme is based on Hirota's bilinear form and certain Riemann theta function formulae. The relations between the periodic wave solutions and soliton solutions are rigorously established. |
| Keywords: | Differential and difference equation Hirota's bilinear method Riemann theta function Periodic wave solution Soliton solution |
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