Bilinearization and Special Solutions to the Discrete Schwarzian KdV Equation

Details Bilinearization and Special Solutions to the Discrete Schwarzian KdV Equation Bilinearization and Special Solutions to the Discrete Schwarzian KdV Equation

2011-02-09

arxiv.org/abs/1102.1829v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages

Scientific paper

Various solutions to the discrete Schwarzian KdV equation are discussed. We first derive the bilinear difference equations of Hirota type of the discrete Schwarzian KP equation, which is decomposed into three discrete two-dimensional Toda lattice equations. We then construct two kinds of solutions in terms of the Casorati determinant. We derive the discrete Schwarzian KdV equation on an inhomogeneous lattice and its solutions by a reduction process. We finally discuss the solutions in terms of the $\tau$ functions of some Painlev\'e systems.

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