Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1997-02-17
Phys. Lett. A, 1997, V.234, p. 91-102.
Nonlinear Sciences
Exactly Solvable and Integrable Systems
23 pages, LaTeX
Scientific paper
10.1016/S0375-9601(97)00592-6
We find time discretizations for the two ''second flows'' of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.
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