Keywords: The nonlinear evolution equations (NLEEs) The generalized Kudryashov method Analytic solutions The Riemann wave equation The Novikov-Veselov equation Solitary wave solutions A B S T R A C T The Riemann wave equation and the Novikov-Veselov equation are interesting nonlinear equations in the sphere of tidal and tsunami waves in ocean, river, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, homogeneous and stationary media etc. In this article, the

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... eralized Kudryashov method is executed to demonstrate the applicability and effectiveness to extract travelling and solitary wave solutions of higher order nonlinear evolution equations (NLEEs) via the earlier stated equations. The technique is enucleated to extract solitary wave solutions in terms of trigonometric, hyperbolic and exponential function. We acquire bell shape soliton, consolidated bell shape soliton, compacton, singular kink soliton, flat kink shape soliton, smooth singular soliton and other types of soliton solutions by setting particular values of the embodied parameters. For the precision of the result, the solutions are graphically illustrated in 3D and 2D. The analytic solutions greatly facilitate the verification of numerical solvers on the stability analysis of the solution. method [5-7], the homogeneous balance method [8], the finite difference method [9], the tanh function method [10], the generalized Kudryashov method [11], the modified simple equation method [12], the dual mode Burgers equation [13], the F-expansion method [14,15], the rational exp-function method [16], Caputo fractional partial derivatives [17], the Durboux transformation method [18], the improved Kudryashov method [19], the first integral method [20], shehu transform [21], the G G ( / ) ' -expansion method [22], the dual-mode Schrodinger equation [23], the tanh-method [24], the −φ ξ exp( ( ))-expansion method [25], the exp-function method [26-28], local fractional homotopy analysis method [29], the trial equation method [30], the improved F-expansion method [31] etc. The generalized Kudryashov method is an important and powerful method to accomplish analytic solutions to the NLEEs. To the best of our understanding, the Riemann wave equation and the NV equation yet have not been investigated by the generalized Kudryashov method. Therefore, in this study, we put in use the generalized Kudryashov method [32-37] to construct the soliton solutions to the Riemann wave equation and the Novikov-Veselov equation. Through implementing the aforesaid method, we found scores of solitary wave solutions. Analytic solutions permit researchers to plan and carry on experiments by