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.

scholarly journals Classification of Exact Solutions for Some Nonlinear Partial Differential Equations with Generalized Evolution

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yusuf Pandir ◽  
Yusuf Gurefe ◽  
Ugur Kadak ◽  
Emine Misirli
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Polynomial Method ◽  
Partial Differential ◽  
Elliptic Solutions ◽  
The One

We obtain the classification of exact solutions, including soliton, rational, and elliptic solutions, to the one-dimensional general improved Camassa Holm KP equation and KdV equation by the complete discrimination system for polynomial method. In discussion, we propose a more general trial equation method for nonlinear partial differential equations with generalized evolution.

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 Reductions and exact solutions of some nonlinear partial differential equations under four types of generalized conditional symmetries

1999 ◽  
Vol 41 (1) ◽  
pp. 1-40 ◽  
Author(s):  
Changzheng Qu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Dynamical Behavior ◽  
Qualitative Properties ◽  
Partial Differential ◽  
Nonclassical Symmetry ◽  
Symmetry Method

AbstractThe generalized conditional symmetry method is applied to study the reduction to finite-dimensional dynamical systems and construction of exact solutions for certain types of nonlinear partial differential equations which have many physically significant applications in physics and related sciences. The exact solutions of the resulting equations are derived via the compatibility of the generalized conditional symmetries and the considered equations, which reduces to solving some systems of ordinary differential equations. For some unsolvable systems of ordinary differential equations, the dynamical behavior and qualitative properties are also considered. To illustrate that the approach has wide application, the exact solutions of a number of nonlinear partial differential equations are also given. The method used in this paper also provides a symmetry group interpretation to some known results in the literature which cannot be obtained by the nonclassical symmetry method due to Bluman and Cole.

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