Bäcklund transformations of -Sine-Gordon systems
arXiv:1704.04412 · doi:10.1142/S0217984917501895
Abstract
In this paper, from the algebraic reductions from the Lie algebra to its commutative subalgebra , we construct the general -Sine-Gordon and -Sinh-Gordon systems which contain many multi-component Sine-Gordon type and Sinh-Gordon type equations. Meanwhile, we give the Bäcklund transformations of the -Sine-Gordon and -Sinh-Gordon equations which can generate new solutions from seed solutions. To see the -systems clearly, we consider the -Sine-Gordon and -Sine-Gordon equations explicitly including their Bäcklund transformations, the nonlinear superposition formula and Lax pairs.
13 Pages, accepted for publication in Modern Physics Letters B