Abstract
In this paper we have discussed the analytical treatment of coupled integrable (2+1)-dimensional nonlinear Schrödinger equation with the help of our newly introduced method extended modified auxiliary equation mapping method(EMAEMM). By using this newly proposed method we have found some new and more general variety of exact traveling wave solutions which are collecting some kind of semi half bright, dark, bright, semi half dark, doubly periodic, combined, periodic, half hark and half bright via three parametric values which is the primary key point of difference of our technique. These results are highly applicable to develop new theories of plasma physics, quantum mechanics, biomedical problems, soliton dynamics, nuclear physics, optical physics, fluid dynamics, electromagnetism, industrial studies, mathematical physics, and in many other natural and physical sciences. For detailed physical dynamical representation of our results we have shown them with graphs in different dimensions using Mathematica 10.4 to get complete understanding in a more efficient manner to observe the behavior of different new dynamical shapes of solutions.