Abstract
Using the Kudryashov and Tanh methods, we have obtained novel exact solutions for the Paraxial Wave Dynamical Equation with Kerr law, including various types of wave solutions. These distinct types of wave solutions have important applications in physics and engineering, and their physical characteristics are well defined. These outcomes are a substantial innovation in the study of water waves in mathematical physics and engineering phenomena. The results we have acquired demonstrate the power and effectiveness of the present techniques.
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