Symbolic Computation of Lax Pairs of Partial Difference Equations using Consistency Around the Cube
نویسندگان
چکیده
A three-step method due to Nijhoff and Bobenko & Suris to derive a Lax pair for scalar partial difference equations (P Es) is reviewed. The method assumes that the P Es are defined on a quadrilateral, and consistent around the cube. Next, the method is extended to systems of P Es where one has to carefully account for equations defined on edges of the quadrilateral. Lax pairs are presented for scalar integrable P Es classified by Adler, Bobenko, and Suris and systems of P Es including the integrable two-component potential Korteweg–de Vries lattice system, as well as nonlinear Schrödinger and Boussinesq-type lattice systems. Previously unknown Lax pairs are presented for P Es recently derived by Hietarinta (J. Phys. A, Math. Theor. 44:165204, 2011). The method is algorithmic and is being implemented in MATHEMATICA.
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عنوان ژورنال:
- Foundations of Computational Mathematics
دوره 13 شماره
صفحات -
تاریخ انتشار 2013