This paper extends the dual-Petrov-Galerkin method proposed by Shen [16] and further developed by Yuan, Shen and Wu [23] to several integrable and non-integrable fifth-order KdV type equations. These fifth-order equations arise in modeling different wave phenomena and involve various nonlinear terms. The method is implemented to compute the solitary wave solutions of these equations and the num...

We develop the inverse scattering transform method for the Novikov equation ut − utxx + 4uux = 3uuxuxx + uuxxx considered on the line x ∈ (−∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann–Hilbert (RH) problem, which in this case is a 3×3 matrix problem. The structure of this RH problem shares many common features with the case of ...

We consider a certain super extension, called the tau-cover, of bihamiltonian integrable hierarchy which contains Hamiltonian structures including both local and non-local ones as odd flows. In particular, we construct tau-cover principal associated with an arbitrary Frobenius manifold, Korteweg-de Vries (KdV) hierarchy. also show that Virasoro symmetries these bihamiltonan hierarchies can be e...

In this article, we have considered Wick-type stochastic Korteweg de Vries (KdV) equation with conformable derivatives. By the help of white noise analysis, Hermit transform and extended G?/G- expansion method, obtained exact travelling wave solutions KdV We applied inverse for soliton then shown how can be presented as Brownian motion functional by an application example.

Unspecified Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: http://doi.org/10.5167/uzh-22229 Originally published at: Bättig, D; Kappeler, T; Mityagin, B (1997). On the Korteweg-de Vries equation: frequencies and initial value problem. Pacific Journal of Mathematics, 181(1):1-55. pacific journal of mathematics Vol. 181, No. 1, 1997 ON THE KORTEWEG-DE VRIES EQUAT...

The existence of a line solitary-wave solution to the water-wave problem with strong surface-tension effects was predicted on the basis of a model equation in the celebrated 1895 paper by D. J. Korteweg and G. de Vries and rigorously confirmed a century later by C. J. Amick and K. Kirchgässner in 1989. A model equation derived by B. B. Kadomtsev and V. I. Petviashvili in 1970 suggests that the ...

Long waves in a current of an inviscid fluid of constant density flowing through a channel ofarbitrary cross section under disturbances of pressure distribution on free surface and obstructors on thewall of the channel are considered. The first order asymptotic approximation of the elevation of the freesurface satisfies a forced Korteweg-de Vries equation when the current is nea...

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.

We solve the Cauchy problem for the Korteweg–de Vries equation with steplike finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite.

In this letter, applying a series of coordinate transformations, we obtain a new class of solutions of the Korteweg–de Vries–Burgers equation, which arises in the theory of ferroelectricity. © 2005 Elsevier Ltd. All rights reserved.