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Time-discretization of soliton equations. (English) Zbl 0961.35135
Levi, Decio (ed.) et al., SIDE III - Symmetries and integrability of difference equations. Proceedings of the 3rd conference, Sabaudia, Italy, May 16-22, 1998. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes. 25, 217-229 (2000).
Summary: A method of time-discretizing soliton equations is presented. The method is based on the bilinear formalism. The soliton equations are transformed into the bilinear forms through the dependent variable transformations. Time-discretization of the bilinear forms are easily performed using the gauge invariance of the bilinear forms but difficulties arise from transforming the bilinear equations into the nonlinear difference equations of ordinary form.
MSC:
35Q51Soliton-like equations
35Q53KdV-like (Korteweg-de Vries) equations
37K40Soliton theory, asymptotic behavior of solutions