numerical investigation of the solitary and periodic waves in the nonlocal discrete manakov system

Solitary waves are interesting phenomena arising in various fields of physics, chemistry, and biology. nonlinear continuous and discrete models supporting wave solutions of solitary behaviour have received increasing attention in recent years. some examples of such integrable systems include korteweg de-vries (kdv) equation, the nonlinear schrödinger (nls) equation, and the manakov system (ms). in this paper, we propose a discrete nonlocal version of the nonlinear manakov system which admits spatial and temporal pt-symmetry. pt-symmetry property gives relevance to various fields in physics and has received a lot of attention in the studies of integrable nonlinear equations. in this work, the time evolution of solitary and periodic wave solutions in the proposed system has been numerically investigated. suitable initial conditions have been considered to construct bright and dark solitons. the variational iteration method (vim) was used to simulate the solution of the system. the error measurement of the simulation demonstrates the efficiency of the numerical method in constructing the different types of wave solutions.