73 research outputs found
Extended Camassa-Holm Hierarchy and Conserved Quantities
An extension of the Camassa-Holm hierarchy is constructed in this letter. The
conserved quantities of the hierarchy are studied and a recurrent formula for
the integrals of motion is derived.Comment: 13 page
Hamiltonian formulation and integrability of a complex symmetric nonlinear system
The integrability of a complex generalisation of the 'elegant' system,
proposed by D. Fairlie and its relation to the Nahm equation and the Manakov
top is discussed.Comment: 8 pages, Physics Letters A (accepted
Empirical balanced truncation of nonlinear systems
Novel constructions of empirical controllability and observability gramians
for nonlinear systems for subsequent use in a balanced truncation style of
model reduction are proposed. The new gramians are based on a generalisation of
the fundamental solution for a Linear Time-Varying system. Relationships
between the given gramians for nonlinear systems and the standard gramians for
both Linear Time-Invariant and Linear Time-Varying systems are established as
well as relationships to prior constructions proposed for empirical gramians.
Application of the new gramians is illustrated through a sample test-system.Comment: LaTeX, 11 pages, 2 figure
Integrable models for shallow water with energy dependent spectral problems
We study the inverse problem for the so-called operators with energy
depending potentials. In particular, we study spectral operators with quadratic
dependance on the spectral parameter. The corresponding hierarchy of integrable
equations includes the Kaup-Bousinesq equation. We formulate the inverse
problem as a Riemann-Hilbert problem with a Z2 reduction group. The soliton
solutions are explicitly obtained.Comment: 17 pages, 3 figure
Poisson structure and Action-Angle variables for the Camassa-Holm equation
The Poisson brackets for the scattering data of the Camassa-Holm equation are
computed. Consequently, the action-angle variables are expressed in terms of
the scattering data.Comment: 20 pages, LaTeX. The original publication is available at
www.springerlink.co
Some Irrational Generalised Moonshine from Orbifolds
We verify the Generalised Moonshine conjectures for some irrational modular
functions for the Monster centralisers related to the Harada-Norton, Held,
and simple groups based on certain orbifolding constraints.
We find explicitly the fixing groups of the hauptmoduls arising in each case
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