Solutions of Two Nonlinear Evolution Equations Using Lie Symmetry and Simplest Equation Methods

Mixed spectral AKNS hierarchy from linear isospectral problem and its exact solutions

“…In the past several decades, many e ective methods have been proposed for obtaining exact solutions of nonlin-*Corresponding Author: Sheng Zhang: School of Mathematics and Physics, Bohai University, Jinzhou 121013, PR China, E-mail: szhangchina@126.com Xu-Dong Gao: School of Mathematics and Statistics, Kashgar University, Kashgar 844066, Peoples's Republic of China ear PDEs, such as the inverse scattering transformation (IST) [1], Hirota's bilinear method [2], Bäcklund transformation [3,4], Painlevé expansion [5], homogeneous balance method [6], similarity transformation method [7,8], ansatz method [9,10], function expansion methods, and some others [11][12][13][14][15][16][17]. Among these methods, the IST [1] is a systematic method.…”

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“…The approximations were; propagation in one direction over a flat bottom with no viscosity, no shear stress and no compressibility under the influence of gravity and surface tension. The CH-DP equation was studied in Mhlanga and Khalique [7] using Lie symmetry method along with the simplest equation method to derive its exact solutions. These solutions were plotted showing a solitary wave behavior.…”