Exact solutions of some nonlinear partial differential equations using functional variable method

Pramana ◽  
2013 ◽  
Vol 81 (2) ◽  
pp. 225-236 ◽  
Author(s):  
A NAZARZADEH ◽  
M ESLAMI ◽  
M MIRZAZADEH
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Variable Method ◽  
Partial Differential ◽  
Functional Variable ◽  
Functional Variable Method

scholarly journals Travelling wave solutions of nonlinear systems of PDEs by using the functional variable method

2015 ◽  
Vol 34 (2) ◽  
pp. 213-229 ◽  
Author(s):  
Hossein Aminikhah ◽  
Amir Hosein Refahi Sheikhani ◽  
Hadi Rezazadeh
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Travelling Wave ◽  
Variable Method ◽  
Boussinesq System ◽  
Wave Transformation ◽  
Partial Differential ◽  
Functional Variable ◽  
Functional Variable Method

In this paper, we will use the functional variable method to construct exact solutions of some nonlinear systems of partial differential equations, including, the (2+1)-dimensional Bogoyavlenskii’s breaking soliton equation, the WhithamBroer-Kaup-Like systems and the Kaup-Boussinesq system. This approach can also be applied to other nonlinear systems of partial differential equations which can be converted to a second-order ordinary differential equation through the travelling wave transformation.

scholarly journals Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2-Expansion Method

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Rational Solutions ◽  
Partial Differential ◽  
Wave Solutions

We apply the G′/G2-expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigonometric solutions, exponential solutions, and rational solutions. The applications of the method are simple, efficient, and reliable by means of using a symbolically computational package. Applying the proposed method to the problems, we have some innovative exact solutions which are different from the ones obtained using other methods employed previously.

scholarly journals New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yusuf Pandir ◽  
Halime Ulusoy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Wave Equations ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Partial Differential ◽  
New Exact Solutions

We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE), we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

B-determining equations: applications to nonlinear partial differential equations

1995 ◽  
Vol 6 (3) ◽  
pp. 265-286 ◽  
Author(s):  
O. V. Kaptsov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Symmetry Groups ◽  
Partial Differential ◽  
Physical Importance

We introduce the concept of B-determining equations of a system of partial differential equations that generalize the defining equations of the symmetry groups. We show how this concept may be applied to obtain exact solutions of partial differential equations. The exposition is reasonable self-contained, and supplemented by examples of direct physical importance, chosen from fluid mechanics.

scholarly journals Classification of Exact Solutions for Generalized Form of Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hasan Bulut
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Generalized Equation ◽  
Polynomial Method ◽  
Partial Differential ◽  
Elliptic Solutions ◽  
Complete Discrimination System

The classification of exact solutions, including solitons and elliptic solutions, to the generalized equation by the complete discrimination system for polynomial method has been obtained. From here, we find some interesting results for nonlinear partial differential equations with generalized evolution.

Sign in / Sign up

Export Citation Format

Share Document