scholarly journals A FAMILY OF THE SPIRAL SOLUTIONS OF THE NONLINEAR KLEIN‐GORDON EQUATION

1998 ◽  
Vol 3 (1) ◽  
pp. 98-103
Author(s):  
V. V. Gudkov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Klein Gordon ◽  
Klein Gordon Equation

A family of the functions, intended for a construction the exact travelling wave solutions of nonlinear partial differential equations, is given. Exact solutions of the Klein‐Gordon equation with a special potential are obtained. The behavior of complex and hypercomplex solutions of the second order is presented.

New Soliton Solutions of Chaffee-Infante Equations Using the Exp-Function Method

2010 ◽  
Vol 65 (3) ◽  
pp. 197-202 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Changbum Chun
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symbolic Computation ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

In this paper, the exp-function method is applied by using symbolic computation to construct a variety of new generalized solitonary solutions for the Chaffee-Infante equation with distinct physical structures. The results reveal that the exp-function method is suited for finding travelling wave solutions of nonlinear partial differential equations arising in mathematical physics

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.

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