scholarly journals Travelling Wave Solutions to the Benney-Luke and the Higher-Order Improved Boussinesq Equations of Sobolev Type

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Ömer Faruk Gözükızıl ◽  
Şamil Akçağıl
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boussinesq Equation ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Higher Order ◽  
Sobolev Type ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions

By using the tanh-coth method, we obtained some travelling wave solutions of two well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation and the higher-order improved Boussinesq equation. We show that the tanh-coth method is a useful, reliable, and concise method to solve these types of equations.

Exact Travelling Wave Solutions of two Important Nonlinear Partial Differential Equations

2014 ◽  
Vol 69 (3-4) ◽  
pp. 155-162 ◽  
Author(s):  
Hyunsoo Kim ◽  
Jae-Hyeong Bae ◽  
Rathinasamy Sakthivel
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Temporal Dynamics ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Kudryashov Method

Coupled nonlinear partial differential equations describing the spatio-temporal dynamics of predator-prey systems and nonlinear telegraph equations have been widely applied in many real world problems. So, finding exact solutions of such equations is very helpful in the theories and numerical studies. In this paper, the Kudryashov method is implemented to obtain exact travelling wave solutions of such physical models. Further, graphic illustrations in two and three dimensional plots of some of the obtained solutions are also given to predict their behaviour. The results reveal that the Kudryashov method is very simple, reliable, and effective, and can be used for finding exact solution of many other nonlinear evolution equations.

scholarly journals Explicit Travelling Wave Solutions to Nonlinear Partial Differential Equations Arise in Mathematical Physics and Engineering

2021 ◽  
Vol 2 (01) ◽  
pp. 58-63
Author(s):  
Muktarebatul Jannah ◽  
Tarikul Islam ◽  
Armina Akter
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Travelling Wave ◽  
Research Field ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Non Linear

To describe the interior phenomena of the mysterious problems around the real world, non-linear partial differential equations (NLPDEs) plays a substantial role, for which construction of analytic solutions of those is most important. This paper stands for a goal to find fresh and wide-ranging solutions to some familiar NLPDEs namely the non-linear cubic Klein-Gordon (cKG) equation and the non-linear Benjamin-Ono (BO) equation. A wave variable transformation is made use to convert the mentioned equations into ordinary differential equations. To acquire the desired precise exact travelling wave solutions to the above-stated equations, the rational -expansion method is employed. Consequently, three types of equipped solutions are successfully come out in the forms of hyperbolic, trigonometric and rational functions in a compatible way. To analyse the physical problems arisen relating to nonlinear complex dynamical systems, our obtained solutions might be most helpful. So far we know, these achieved solutions are different than those in the literature. The applied method is efficient and reliable which might further be used to find different and novel solutions to many other NLPDEs successfully in research field.

scholarly journals Exact Traveling Wave Solutions to Benney- Luke Equation

2018 ◽  
Vol 37 ◽  
pp. 1-14
Author(s):  
Zahidul Islam ◽  
Mohammad Mobarak Hossain ◽  
Md Abu Naim Sheikh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Sobolev Type ◽  
Travelling Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

By using the improved (G¢/G) -expansion method, we obtained some travelling wave solutions of well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation. We show that the improved (G¢/G) -expansion method is a useful, reliable, and concise method to solve these types of equations.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 1-14

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