424 research outputs found
An abstract disintegration theorem
A Strassen-type disintegration theorem for convex cones with localized order structure is proved. As an example a flow theorem for infinite networks is given
Integrable Theory of the Perturbation Equations
An integrable theory is developed for the perturbation equations engendered
from small disturbances of solutions. It includes various integrable properties
of the perturbation equations: hereditary recursion operators, master
symmetries, linear representations (Lax and zero curvature representations) and
Hamiltonian structures etc. and provides us a method to generate hereditary
operators, Hamiltonian operators and symplectic operators starting from the
known ones. The resulting perturbation equations give rise to a sort of
integrable coupling of soliton equations. Two examples (MKdV hierarchy and KP
equation) are carefully carried out.Comment: 27 pages, latex, to appear in Chaos, Soliton & Fractal
Variational derivation of the Camassa-Holm shallow water equation
We describe the physical hypothesis in which an approximate model of water
waves is obtained. For an irrotational unidirectional shallow water flow, we
derive the Camassa-Holm equation by a variational approach in the Lagrangian
formalism.Comment: 10 page
On symmetries of KdV-like evolution equations
The -dependence of the symmetries of (1+1)-dimensional scalar
translationally invariant evolution equations is described. The sufficient
condition of (quasi)polynomiality in time of the symmetries of evolution
equations with constant separant is found. The general form of time dependence
of the symmetries of KdV-like non-linearizable evolution equations is
presented.Comment: LaTeX, 8 pages, no figures, very minor change
The Camassa-Holm Equation: A Loop Group Approach
A map is presented that associates with each element of a loop group a
solution of an equation related by a simple change of coordinates to the
Camassa-Holm (CH) Equation. Certain simple automorphisms of the loop group give
rise to Backlund transformations of the equation. These are used to find
2-soliton solutions of the CH equation, as well as some novel singular
solutions.Comment: 19 pages, 7 figures; LaTeX with psfi
A method for obtaining Darboux transformations
In this paper we give a method to obtain Darboux transformations (DTs) of
integrable equations. As an example we give a DT of the dispersive water wave
equation. Using the Miura map, we also obtain the DT of the Jaulent-Miodek
equation. \end{abstract
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