Algebraic Discretization of the Camassa-Holm and Hunter-Saxton Equations
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چکیده
منابع مشابه
Algebraic Discretization of the Camassa-Holm and Hunter-Saxton Equations
The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H and Ḣ right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a right-invariant metric on the infinitedimensional group of diffeomorphisms preserving the volume el...
متن کاملThe Soliton Content of the Camassa–Holm and Hunter–Saxton Equations
The notion of a scalar equation describing pseudo-spherical surfaces is reviewed. It is shown that if an equation admits this structure, the existence of conservation laws, symmetries, and quadratic pseudo-potentials, can be studied by geometrical means. As an application, it is pointed out that the important Camassa–Holm and Hunter–Saxton equations possess features considered to be characteris...
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We consider N=2 supersymmetric extensions of the Camassa-Holm and HunterSaxton equations. We show that they admit geometric interpretations as Euler equations on the superconformal algebra of contact vector fields on the 1|2dimensional supercircle. We use the bi-Hamiltonian formulation to derive Lax pairs. Moreover, we present some simple examples of explicit solutions. As a byproduct of our an...
متن کاملEquations of the Camassa-Holm Hierarchy
The squared eigenfunctions of the spectral problem associated with the CamassaHolm (CH) equation represent a complete basis of functions, which helps to describe the inverse scattering transform for the CH hierarchy as a generalized Fourier transform (GFT). All the fundamental properties of the CH equation, such as the integrals of motion, the description of the equations of the whole hierarchy...
متن کاملWell-posedness of modified Camassa–Holm equations
Article history: Received 4 April 2008 Revised 11 January 2009 Available online 28 February 2009
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ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2008
ISSN: 1776-0852
DOI: 10.2991/jnmp.2008.15.s2.1