Related papers: Newell-Whitehead-Segel Equation: An Exact, General…
In this monograph, two sets of parabolic differential equations are studied, each with nonlinear medium response. The equations are generally referred to as "Newell-Whitehead-Segel equation," which model a wide variety of nonlinear…
In the present work, we use the Adomian Decomposition method to find the approximate solution for some cases of the Newell whitehead segel nonlinear differential equation which was solved previously with exact solution by the Homotopy…
Previous analysis of the Newell-Whitehead-Segel equation proved the best solution is null; although, the method of solution generated complex nested integrals, therefore, difficult to analyze \cite{NWSgen,NWS2020}. Recent insights into the…
An explicit analytic solution to the nonlinear differential equation d^k y (--) ^n = y^l dx^kk is obtained for arbitrary integer values of k, l and n.
This paper is dedicated to present an exact solution for a nonlinear differential equation so-called Abel equation. This equation was known as one of the group of unsolvable differential equations. The present method is applicable for any…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a…
A class of the Newell-Whitehead-Segel equations (also known as generalized Fisher equations and Newell-Whitehead equations) is studied with Lie and "nonclassical" symmetry points of view. The classifications of Lie reduction operators and…
There are few approaches to the solution of a system of nonlinear differential equations in partial derivatives, for example $\cite{NK87} - \cite{EK98}$. In our paper we propose an approach that was used to solve the Navier-Stokes equations…
In this paper, we study the existence and non-existence of entire solutions of certain non-linear delay-differential equations.
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the generalized Brethenton equation are given.
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
An equation to describe nearly one-dimensional traveling-waves patterns is put forward. This is a dispersive generalization of the classical Newell-Whitehead-Segel (NWS) equation. Transverse stability of plane waves is considered within the…
New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…
Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with essentially the same toolbox, when one looks for analytic solutions in closed form. The basic tool…
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of the Newton polygons corresponding to nonlinear differential equations. It allows one to express exact solutions…
In this paper, we investigate the existence and nonexistence of entire solutions to a general class of Cauchy problems in the positive half line. Our results provide a unified approach to proving sharp local and entire solvability of…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and…
In this paper, solutions of the generic non-compact Weyl equation are obtained. In particular, by identifying a suitable similarity transformation and introducing a non-trivial change of variables we are able to implement azimuthal…