Extended Painlevé Expansion, Nonstandard Truncation and Special Reductions of Nonlinear Evolution Equations
نویسنده
چکیده
To study a nonlinear partial differential equation (PDE), the Painlev́e expansion developed by Weiss, Tabor and Carnevale (WTC) is one of the most powerful methods. In this paper, using any singular manifold, the expansion series in the usual Painlev́e analysis is shown to be resummable in some different ways. A simple nonstandard truncated expansion with a quite universal reduction function is used for many nonlinear integrable and nonintegrable PDEs such as the Burgers, Korteweg de-Vries (KdV), Kadomtsev-Petviashvli (KP), Caudrey-Dodd-GibbonSawada-Kortera (CDGSK), Nonlinear Schrödinger (NLS), Davey-Stewartson (DS), Broer-Kaup (BK), KdV-Burgers (KdVB), , sine-Gordon (sG) etc.
منابع مشابه
Painlevé Properties and Exact Solutions of the Generalized Coupled KdV Equations
The generalized coupled Korteweg-de Vries (GCKdV) equations as one case of the four-reduction of the Kadomtsev-Petviashvili (KP) hierarchy are studied in details. The Painlevé properties of the model are proved by using the standard Weiss-Tabor-Carnevale (WTC) method, invariant, and perturbative Painlevé approaches. The meaning of the negative index k =−2 is shown, which is indistinguishable fr...
متن کاملModified F-Expansion Method Applied to Coupled System of Equation
A modified F-expansion method to find the exact traveling wave solutions of two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...
متن کاملApplication of the new extended (G'/G) -expansion method to find exact solutions for nonlinear partial differential equation
In recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. One such method is known as the new extended (G'/G)-expansion method and was proposed by Roshid et al. In this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (NLPDEs), namely the Benjamin-Ono equation. It is est...
متن کاملPositivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations
Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...
متن کاملNonstandard explicit third-order Runge-Kutta method with positivity property
When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...
متن کامل