scholarly journals Asymptotic stability of traveling wave solutions for nonlocal viscous conservation laws with explicit decay rates

2018 ◽  
Vol 18 (2) ◽  
pp. 923-946 ◽  
Author(s):  
Franz Achleitner ◽  
Yoshihiro Ueda
Keyword(s):  
Asymptotic Stability ◽  
Conservation Laws ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Decay Rates ◽  
Wave Solutions ◽  
Viscous Conservation Laws

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.

scholarly journals Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Multiplier Method ◽  
Two Dimensional ◽  
Wave Solutions ◽  
Conservation Theorem ◽  
Bbm Equation

We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the(G'/G)-expansion method.

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