Remarks on traveling wave solutions of non-linear diffusion equations

1976 ◽  
pp. 77-89 ◽  
Author(s):  
C. Conley ◽  
Joel Smoller
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Diffusion Equations ◽  
Linear Diffusion ◽  
Wave Solutions ◽  
Non Linear

scholarly journals Application of the modified simple equation method for solving two nonlinear time-fractional long water wave equations

2021 ◽  
Vol 67 (6 Nov-Dec) ◽  
Author(s):  
Gizel Bakicierler ◽  
Suliman Alfaqeih ◽  
Emine Misirli
Keyword(s):  
Traveling Wave ◽  
Water Waves ◽  
Water Wave ◽  
Wave Equations ◽  
Traveling Wave Solutions ◽  
Simple Equation ◽  
Wave Solutions ◽  
Non Linear ◽  
Package Program ◽  
Modified Simple Equation Method

Recently, non-linear fractional partial differential equations are used to model many phenomena in applied sciences and engineering. In this study, the modified simple equation scheme is implemented to obtain some new traveling wave solutions of the non-linear conformable time-fractional approximate long water wave equation and the non-linear conformable coupled time-fractional Boussinesq-Burger equation, which are used in the expression of shallow-water waves. The time- fractional derivatives are described in terms of conformable fractional derivative sense. Consequently, new exact traveling wave solutions of both equations are achieved. The graphics and correctness of the wave solutions are obtained with the Mathematica package program.

scholarly journals Exact Traveling Wave Solutions of Modified Liouville Equation

2016 ◽  
Vol 35 ◽  
pp. 135-143
Author(s):  
Md Abdus Salam ◽  
Md Obayedullah ◽  
Md Shajib Ali
Keyword(s):  
Linear Equation ◽  
Liouville Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Approximate Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Non Linear Equation ◽  
Non Linear ◽  
Optimum Solution

In this paper fuzzy version of secant method has been introduced to obtain approximate solutions of a fuzzy non-linear equation. Graphical representations of the approximate solutions have also been shown. The idea of converging to the root to the desired degree of accuracy, which is the optimum solution, of a fuzzy non-linear equation has been focused.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 135-143

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