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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.
For the entire collection see [Zbl 0943.00052].

MSC:

35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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