scholarly journals Resonant multiple wave solutions for a (3+1)-dimensional nonlinear evolution equation by linear superposition principle

2017 ◽  
Vol 73 (10) ◽  
pp. 2339-2343 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Wen-Xiu Ma
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Superposition Principle ◽  
Linear Superposition ◽  
Multiple Wave ◽  
Wave Solutions ◽  
Linear Superposition Principle

Multiple-Wave Solutions to Generalized Bilinear Equations in Terms of Hyperbolic and Trigonometric Solutions

2017 ◽  
Vol 18 (5) ◽  
pp. 395-401
Author(s):  
Ömer Ünsal ◽  
Wen-Xiu Ma ◽  
Yujuan Zhang
Keyword(s):  
Necessary Conditions ◽  
Superposition Principle ◽  
Trigonometric Function ◽  
Linear Superposition ◽  
Multiple Wave ◽  
Wave Solutions ◽  
Trigonometric Function Solutions ◽  
Sufficient And Necessary Conditions ◽  
Linear Superposition Principle ◽  
Bilinear Equations

AbstractThe linear superposition principle is applied to hyperbolic and trigonometric function solutions to generalized bilinear equations. We determine sufficient and necessary conditions for the existence of linear subspaces of hyperbolic and trigonometric function solutions to generalized bilinear equations. By using weights, three examples are given to show applicability of our theory.

Traveling wave solutions and conservation laws of a generalized Kudryashov–Sinelshchikov equation

2019 ◽  
Vol 25 (2) ◽  
pp. 211-217 ◽  
Author(s):  
Ben Muatjetjeja ◽  
Abdullahi Rashid Adem ◽  
Sivenathi Oscar Mbusi
Keyword(s):  
Heat Transfer ◽  
Evolution Equation ◽  
Conservation Laws ◽  
Traveling Wave ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Pressure Waves ◽  
Wave Solutions ◽  
Kudryashov Method

Abstract Kudryashov and Sinelshchikov proposed a nonlinear evolution equation that models the pressure waves in a mixture of liquid and gas bubbles by taking into account the viscosity of the liquid and the heat transfer. Conservation laws and exact solutions are computed for this underlying equation. In the analysis of this particular equation, two approaches are employed, namely, the multiplier method and Kudryashov method.

The Multiple Exp-Function Method and the Linear Superposition Principle for Solving the (2+1)-Dimensional Calogero–Bogoyavlenskii–Schiff Equation

2015 ◽  
Vol 70 (9) ◽  
pp. 775-779 ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Function Method ◽  
Superposition Principle ◽  
Solitary Wave Solutions ◽  
Linear Superposition ◽  
Wave Solutions ◽  
Linear Superposition Principle

AbstractIn this article, the multiple exp-function method and the linear superposition principle are employed for constructing the exact solutions and the solitary wave solutions for the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. With help of Maple and by using the multiple exp-method, we can get exact explicit one-wave, two-wave, and three-wave solutions, which include one-soliton-, two-soliton-, and three-soliton-type solutions. Furthermore, we apply the linear superposition principle to find n-wave solutions of the CBS equation. Two cases with specific values of the involved parameters are plotted for each two-wave and three-wave solutions.

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