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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.

35L70Nonlinear second-order hyperbolic equations
39A14Partial difference equations
39A23Periodic solutions (difference equations)
35C07Traveling wave solutions of PDE
35C08Soliton solutions of PDE
Full Text: DOI
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