Conservation laws, optical molecules, modulation instability and Painlevé analysis for the Chen–Lee–Liu model

In this paper, we will compute the conservation laws (CLs) of Chen–Lee–Liu equation (CLLE) with the help of scaling invariance technique. We will use Euler and Homotopy operators for the evaluation of conserved densities and fluxes. We will also obtain optical dromions with the help of Unified method (UM). By using this method, we will get domain walls, solitary wave and elliptic wave solutions. Moreover, we will investigate the stability as well as the integrability of the governing model by using linear stability technique and Painlevé analysis respectively.