Korteweg–De Vries equation

The Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow water surfaces.

The Korteweg-de Vries Equation: History, exact Solutions, and ...

Travelling waves as solutions to the Korteweg-de Vries equation (KdV) which is a non-linear Partial. Differential Equation (PDE) of third order have been of ...

Introduction to KdV - WikiWaves

The KdV equation posesses travelling wave solutions. One particular travelling wave solution is called a soltion and it was discovered ...

Topic 2: The Korteweg-de Vries Equation - Mathematics | U-M LSA

The KdV equation. Symmetry properties. An equation for u(x, t) is said to be a Korteweg-de Vries. (KdV) equation (Korteweg and de Vries, 1895) if it is of ...

The Korteweg-de Vries Equation - ETH Zürich

This report is concerned with a description of the Korteweg-de Vries equation, or KdV equation for short, focusing on special properties of its solutions.

Korteweg-De Vries Equation - an overview | ScienceDirect Topics

Korteweg-de Vries (KdV) equation is a very famous nonlinear equation, the equation and equations derived from itself have been widely studied.

Solitons in the Korteweg-de Vries Equation (KdV Equation)

The Korteweg-de Vries Equation (KdV equation) describes the theory of water waves in shallow channels, such as a canal. It is a non-linear equation which ...

Method for Solving the Korteweg-deVries Equation

A method for solving the initial-value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant ...

[PDF] Korteweg-de Vries Equation - Semantic Scholar

The Korteweg-de Vries (KdV) equation, given here in canonical form, u t + 6uu x + u xxx = 0 , (1) is widely recognised as a paradigm for the description of ...

[math/0602661] On the origin of the Korteweg-de Vries equation

Abstract page for arXiv paper math/0602661: On the origin of the Korteweg-de Vries equation.

The Korteweg–deVries Equation: A Survey of Results | SIAM Review

The Korteweg–de Vries equation is a nonlinear partial differential equation arising in the study of a number of different physical systems.

Korteweg‐de Vries Equation and Generalizations. III. Derivation of ...

The Korteweg‐de Vries equation and the Burgers equation are derived for a wide class of nonlinear Galilean‐invariant systems under the weak‐nonlinearity and ...

The Korteweg-de Vries equation and water waves. Part 2 ...

The KdV equation is found to predict accurately the number of evolving solitons and their shapes for initial data whose asymptotic characteristics develop in ...

KdV hierarchy - Wikipedia

In mathematics, the KdV hierarchy is an infinite sequence of partial differential equations which contains the Korteweg–de Vries equation.

Complexiton solutions to the Korteweg–de Vries equation

Such solutions presented in Theorem 2 are called complexiton solutions of higher order, and the order is defined to be the total sum of mi and ni, 1⩽i⩽N.

Korteweg–de Vries (KdV) equation - Soliton solution as ... - YouTube

Considering plane wave solutions to the KdV equation I convert the nonlinear third order partial differential equation in to second order ...

Korteweg de-Vries Equation - SpringerLink

In this chapter we consider weakly nonlinear long waves. Here the basic paradigm is the well-known Korteweg-de Vries equation and its solitary wave solution ...

Korteweg-de Vries Equation

Korteweg-de Vries Equation. The Korteweg-de Vries (KdV) equation is the partial differential equation, derived by Korteweg and de Vries [14] to describe ...

Korteweg-de Vries Equation -- from Wolfram MathWorld

The partial differential equation u_t+u_(xxx)-6uu_x=0 (1) (Lamb 1980; Zwillinger 1997, p. 175), often abbreviated "KdV." This is a nondimensionalized ...

Derivation of the KdV equation for surface and internal waves

To first order we recover the linear long wave solutions, and to second order we find that the amplitude evolves according to the KdV equation. The extended KdV ...