In this study, the localfractional variational iterationmethod (LFVIM) and the localfractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractionalderivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very ef...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...

The transformation of a weakly nonlinear interfacial solitary wave in an ideal twolayer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a we...

In the course of the years the names of Korteweg and de Vries have come to be closely associated. The equation which is named after them plays a fundamental role in the theory of nonlinear partial differential equations. What are the origins of the doctoral dissertation of De Vries and of the Korteweg-de Vries paper? Bastiaan Willink, a distant relative of both of these mathematicians, has soug...

The periodic flag manifold (in the Sato Grassmannian context) description of the modified Korteweg–de Vries hierarchy is used to analyse the translational and scaling self–similar solutions of this hierarchy. These solutions are characterized by the string equations appearing in the double scaling limit of the symmetric unitary matrix model with boundary terms. The moduli space is a double cove...

This paper is concerned with interacting wave packet dynamics for long waves. The Kortweg-de Vries equation is the most well-known model for weakly nonlinear long waves. Although the dynamics of a single wave packet in this model is governed by the defocusing nonlinear Schrödinger equation, implying that a plane wave is modulationally stable, the dynamics of two interacting wave packets is gove...

It is well known that from two-dimensional lattice equations one can derive one-dimensional lattice equations by imposing periodicity in some direction. In this paper we generalize the periodicity condition by adding a symmetry transformation and apply this idea to autonomous and nonautonomous lattice equations. As results of this approach, we obtain new reductions of the discrete potential Kor...