Darboux transformation and multi-soliton solutions of the discrete sine-Gordon equation

We study the discrete Darboux transformation and construct multi-soliton solutions in terms of the ratio of determinants for the integrable discrete sine-Gordon equation. We also calculate explicit expressions of single-, double-, triple-, and quadruple-soliton solutions as well as single- and double-breather solutions of the discrete sine-Gordon equation. The dynamical features of discrete kinks and breathers are also illustrated.

Soliton solutions, conservation laws and modulation instability for the discrete coupled modified Korteweg–de Vries equations

In this paper, the discrete coupled modified Korteweg–de Vries equations are systematically investigated. Based on the Lax pair, N-fold discrete Darboux transformation, discrete soliton solutions, conservation laws and modulation instability are analyzed and presented.