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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 sufficiently rapidly as
An energy principle for hydromagnetic stability problems
The problem of the stability of static, highly conducting, fully ionized plasmas is investigated by means of an energy principle developed from one introduced by Lundquist. The derivation of the
Korteweg‐de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
With extensive use of the nonlinear transformations presented in Paper I of the series, a variety of conservation laws and constants of motion are derived for the Korteweg‐de Vries and related
Exact Nonlinear Plasma Oscillations
The problem of a one-dimensional stationary nonlinear electrostatic wave in a plasma free from interparticle collisions is solved exactly by elementary means. It is demonstrated that, by adding
Maximal extension of Schwarzschild metric
New similarity reductions of the Boussinesq equation
Some new similarity reductions of the Boussinesq equation, which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is
Kink dynamics in the highly discrete sine-Gordon system
Abstract We study kink dynamics in a very discrete sine-Gordon system where the kink width is of the order of the lattice spacing. Numerical simulations exhibit new properties of kinks in this case:
Equilibrium of a Magnetically Confined Plasma in a Toroid
A variety of properties are derived satisfied by any static equilibrium of a plasma governed by the well‐known magnetostatic equations. Some of these are local and quite trivial. Others involve