The bifurcation and exact peakons, solitary and periodic wave solutions for the Kudryashov–Sinelshchikov equation

A improved F-expansion method and its application to Kudryashov-Sinelshchikov equation

“…Some new exact solutions expressed by exponential function, hyperbolic functions for the Kudryashov–Sinelshchikov equation, are derived by using this method. The results of references have been enriched. From the derivation of the exact solutions, it is easy to see that the improved F‐expansion method is a useful tool to explore the exact solution for PDE.…”

Local conservation laws, symmetries, and exact solutions for a Kudryashov‐Sinelshchikov equation

“…First of all, many papers have been focused on the special case b =1, d = e =0. () Tu et al classified the Lie symmetries of Equation for those specific values of the parameters. In addition, they constructed the optimal system of subalgebras and obtained exact solutions by using the symmetry reductions.…”

“…These solutions include the form of Jacobi elliptic functions, hyperbolic functions, trigonometric, and rational functions. In He et al,() by using the bifurcation method of dynamical systems and the method of phase portraits analysis, the authors show the limit forms of periodic loop solutions contain loop soliton solutions, smooth periodic wave solutions, and periodic cusp wave solutions as well as the existence of peakons, solitary waves, and nonsmooth periodic waves. Randrüüt and Braun showed that the travelling wave solutions of the KS Equation can be derived from corresponding solutions of a generalized KdV equation.…”

Lie symmetry analysis and exact explicit solutions of three-dimensional Kudryashov–Sinelshchikov equation

“…(1) is called Kudryashov-Sinelshchikov equation and is for describing the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer, it is generalization of the KdV and the BKdV equation and similar but not identical to the Camassa-Holm equation. Equation (1) was studied by many researchers in 2 various methods [2][3][4][5][6][7][8][9]. Further, in the more realistic situations, the following three-dimensional…”