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 generalized 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.

黎曼波方程和Novikov-Veselov方程是海洋，河流，等离子中的离子和磁声波，传输线中的电磁波，均匀介质和固定介质等中的潮汐和海啸波领域中有趣的非线性方程。文章中，执行了广义Kudryashov方法，以证明通过较早提出的方程式来提取高阶非线性演化方程（NLEE）的行波和孤波解的适用性和有效性。运用该技术提取了三角函数，双曲函数和指数函数方面的孤立波解。我们获得钟形孤子，固结钟形孤子，compacton，奇异扭结孤子，平扭结孤子，通过设置具体参数的特定值，可以平滑奇异孤子和其他类型的孤子解。为了获得精确的结果，以3D和2D形式图解说明了解决方案。解析解极大地方便了数值求解器对稳定性分析的验证。