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The nonlinear Schrödinger equation and the coupled Burgers equation illustrate the status of quantum particles, shock waves, acoustic transmission and traffic flow. Therefore these equations are physically significant in their own right. In this article, the new auxiliary equation method has been contrivanced in order to rummage exact wave solutions to previously stated nonlinear evolution equations (NLEEs). We have developed ample soliton solutions and have to do with the physical importance of the acquired solutions by setting the specific values of the embodied parameters through portraying figures and deciphered the physical phenomena. It has been established that the executed method is powerful, skilled to examine NLEEs, compatible to computer algebra and provides further general wave solutions. Thus, the investigation of exact solutions to other NLEES through the new auxiliary method is prospective and deserves further research.

Outset of multiple soliton solutions to the nonlinear Schrödinger equation and the coupled Burgers equation