Abstract
In this article we have presented the analytical analysis of coupled integrable (2+1)-dimensional Maccari System with the aid of newly developed technique named as an extended modified auxiliary equation mapping method. As a result we have found a variety of new families of exact traveling wave solutions including triangular-type solutions, periodic and doubly periodic like solutions, combined soliton like solutions, kink and anti kink type soliton like solutions with the help of three parameters which is the key importance of this method. Maccari System is a well known model to define the dynamics of isolated waves, localized in a very small part of space in different fields of physics such as quantum mechanics, hydrodynamics, plasma physics, quantum field theory to study the dynamics of Langmuir solitons which are appearing in the nonlinear optics. For physical description of our newly obtained solutions we have expressed them graphically using Mathematica 10.4 to explain more efficiently the behavior of different shapes of solutions. Also the computational work and efficiency of the method demonstrates the reliability, straightforwardness, and simplicity of the method for solving other nonlinear complicated partial differential equations.