On $$\varvec{\mathcal {PT}}$$-symmetric semi-discrete coupled integrable dispersionless system

Abstract

In this work, we have proposed a $$\mathcal {PT}$$-symmetric reverse space-time nonlocal semi-discrete coupled integrable dispersionless system by discretization of associated linear eigenvalue problem. Darboux transformation has been applied to construct nontrivial solutions in terms of determinants. To elaborate the dynamics of solutions, explicit expressions of first two nontrivial solutions are computed. We analyze both symmetry broken and preserving solutions for generalized and $$\mathcal {PT}$$-symmetric reverse space-time nonlocal semi-discrete coupled integrable dispersionless systems, respectively. We also obtain first two nontrivial soliton solutions of local semi-discrete coupled integrable dispersionless system under certain condition on the spectral parameters.