Separability and a Lax Pair for the c_{2}{(1)} Toda lattice (Global Journal of Science Frontier Research, 2024)
We consider the Toda lattice associated to the twisted affine Lie algebra 2 (1) . It is well known that this system is a two-dimensional algebraic completely integrable system. By using algebraic geometric methods, we give a linearisation of the system by determining the linearizing variables. This allows us to explain a morphism between this system and the Mumford system. Finally, a Lax representation in terms of 2 x 2 matrices is constructed for this system.
Keywords: toda lattice; integrable system; linearisation; lax representation