On soliton solutions of multi-component semi-discrete short pulse equation

The short pulse (SP) equation is an integrable equation. Multi-component generalizations of the SP equation are important for describing the polarization or anisotropic effects in optical fibers. An integrable semi-discretization of multi-component SP equation via Lax pair and Darboux transformation (DT) has been presented. Wederive a Lax pair representation for the multi-component semidiscrete short pulse (sdSP) equation in the form of a block matrices by generalizing the 2 x 2 Lax pair matrices to the case of 2(N) x 2(N). ADTis studied for the multi-component sdSP equation and is used to compute soliton solutions of the system. Further, by expanding quasideterminants, we compute cuspon-soliton, smooth-soliton and loop-soliton solutions of the complex sdSP equation.