scholarly journals Eventual periodicity for the KdV equation on a half-line

2007 ◽  
Vol 227 (2) ◽  
pp. 105-119 ◽  
Author(s):  
Jie Shen ◽  
Jiahong Wu ◽  
Juan-Ming Yuan
Keyword(s):  
Kdv Equation ◽  
Half Line ◽  
The Kdv Equation

A Neumann problem for the KdV equation with Landau damping on a half-line

2011 ◽  
Vol 74 (14) ◽  
pp. 4682-4697
Author(s):  
Felipe Benitez ◽  
Elena I. Kaikina
Keyword(s):  
Neumann Problem ◽  
Kdv Equation ◽  
Landau Damping ◽  
Half Line ◽  
The Kdv Equation

Boundary value problem for the KDV equation on a half-line

1997 ◽  
Vol 110 (1) ◽  
pp. 78-90 ◽  
Author(s):  
V. E. Adler ◽  
L. T. Habibullin ◽  
A. B. Shabat
Keyword(s):  
Boundary Value Problem ◽  
Kdv Equation ◽  
Boundary Value ◽  
Half Line ◽  
The Kdv Equation

Integrable Models

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Fluid Mechanics ◽  
Soliton Solution ◽  
Water Waves ◽  
Heisenberg Model ◽  
Kdv Equation ◽  
Short Review ◽  
Lax Pair ◽  
Shallow Water Waves ◽  
Initial Value ◽  
The Kdv Equation

Some exceptional situations in fluid mechanics can be modeled by equations that are analytically solvable. The most famous example is the Korteweg–de Vries (KdV) equation for shallow water waves in a channel. The exact soliton solution of this equation is derived. The Lax pair formalism for solving the general initial value problem is outlined. Two hamiltonian formalisms for the KdV equation (Fadeev–Zakharov and Magri) are explained. Then a short review of the geometry of curves (Frenet–Serret equations) is given. They are used to derive a remarkably simple equation for the propagation of a kink along a vortex filament. This equation of Hasimoto has surprising connections to the nonlinear Schrödinger equation and to the Heisenberg model of ferromagnetism. An exact soliton solution is found.

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