Casorati Determinant Solution for the Relativistic Toda Lattice Equation

Details Casorati Determinant Solution for the Relativistic Toda Lattice Equation Casorati Determinant Solution for the Relativistic Toda Lattice Equation

1993-04-22

arxiv.org/abs/solv-int/9304002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages in plain Tex

Scientific paper

10.1063/1.530298

The relativistic Toda lattice equation is decomposed into three Toda systems, the Toda lattice itself, B\"acklund transformation of Toda lattice and discrete time Toda lattice. It is shown that the solutions of the equation are given in terms of the Casorati determinant. By using the Casoratian technique, the bilinear equations of Toda systems are reduced to the Laplace expansion form for determinants. The $N$-soliton solution is explicitly constructed in the form of the Casorati determinant.

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