相关论文: A Note On 3Solitary Wave Solutions of the Compound…
In this paper, we study a compound Korteweg-de Vries-Burgers equation with a higher-order nonlinearity. A class of solitary wave solutions is obtained by means of a series expansion.
Travelling-wave solutions of the standard and compound form of Korteweg-de Vries-Burgers equations are found using factorizations of the corresponding reduced ordinary differential equations. The procedure leads to solutions of Bernoulli…
We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries equation (KdV). We show that this approximation, which we call KdVH, possesses a rich variety of solutions, including solitary wave solutions that approximate…
We present new periodic, kink-like and soliton-like travelling wave solutions to the hyperbolic generalization of Burgers equation. To obtain them, we employ the classical and generalized symmetry methods and the ansatz-based approach
The goal of this work is to determine classes of traveling Solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz.
New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries…
The relevance of perturbed forms of the Korteweg-de Vries equation to a range of physical problems is discussed. Solutions which are perturbations of solitary travelling wave solutions are then considered, focussing predominantly on the…
The goal of this work is to determine whole classes of solitary wave solutions general for wave equations.
In this paper we propose a reduction procedure for determining generalized travelling waves for first order quasilinear hyperbolic nonhomogeneous systems. The basic idea is to look for solutions of the governing model which satisfy a…
In this article, we follow an idea that is opposite to the idea of Hopf and Cole: we use transformations in order to transform simpler linear or nonlinear differential equations (with known solutions) to more complicated nonlinear…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
In the framework of hyperbolic conservation laws regularised by including diffusive and dispersive terms, we study monotone travelling waves for the generalised Rosenau-Korteweg de Vries equation. We establish existence as well as linear…
We study the traveling wave solutions of the Burgers-Huxley equation from a geometric point of view via the qualitative theory of ordinary differential equations. By using the Poincar\'e compactification we study the global phase portraits…
We construct solitary waves for the fractional Korteweg-De Vries type equation $u_t + (\Lambda^{-s}u + u^2)_x = 0$, where $\Lambda^{-s}$ denotes the Bessel potential operator $(1 + |D|^2)^{-\frac{s}{2}}$ for $s \in (0,\infty)$. The approach…
The method of simplest equation is applied for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. The used…
We emphasize that construction of travelling wave solutions for partial differential equations is a problem of considerable interest and thus introduce a simple algebraic method to generate such solutions for equations in the Burgers…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…
New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.
We add a theorem to [J. Differential Equations 257 (2014), no. 3, 720--758] by F. Achleitner, C.M. Cuesta and S. Hittmeir. In that paper we studied travelling wave solutions of a Korteweg-de Vries-Burgers type equation with a non-local…