| Summary: | In this article, we construct the traveling wave and elliptic function solutions of some special nonlinear evolution equations which are arising in mathematical physics, solid-state physics, fluid flow, fluid dynamics, nonlinear optics, electromagnetic waves, quantum field theory etc. We employed modified extended direct algebraic method to construct the traveling wave and elliptic function solutions of Dodd-Bullough-Mikhailov equation, two-dimensional Sine-Gordon equation and coupled Schrödinger-KdV equation. The obtained analytical solutions in various form of each equation have different physical structures which are also presented graphically. The advantage of the current method that is simple, direct, elementary and concise. This method can be employed with a wider applicability for handling several other types of nonlinear wave equations. Keywords: Modified extended direct algebraic method, Travelling wave solutions, Elliptic function solutions, Dodd-Bullough-Mikhailov equation, Two-dimensional Sine-Gordon equation, Coupled Schrödinger-KdV equation
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