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On the periodic solutions for both nonlinear differential and difference equations: a unified approach. (English) Zbl 1238.35060

Summary: 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 periodic wave solutions and soliton solutions are rigorously established.

MSC:

35L70 Second-order nonlinear hyperbolic equations
39A14 Partial difference equations
39A23 Periodic solutions of difference equations
35C07 Traveling wave solutions
35C08 Soliton solutions
14K25 Theta functions and abelian varieties
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