Backlund transformations of Z(n)-sine-Gordon systems

摘要

In this paper, from the algebraic reductions from the Lie algebra gl (n,C) to its commutative subalgebra Z(n), we construct the general Z(n)-sine-Gordon and Z(n)-sinh-Gordon systems which contain many multi-component sine-Gordon type and sinh-Gordon type equations. Meanwhile, we give the Backlund transformations of the Z(n)-sine-Gordon and Z(n)-sinh-Gordon equations which can generate new solutions from seed solutions. To see the Z(n)-systems clearly, we consider the Z2-sine-Gordon and Z3-sine-Gordon equations explicitly including their Backlund transformations, the nonlinear superposition formula and Lax pairs.