Related papers: On A Recently Proposed Relation Between oHS and It…

We develop a systematic procedure for constructing soliton solutions of an integrable two-component Camassa-Holm (CH2) system. The parametric representation of the multisoliton solutions is obtained by using a direct method combined with a…

We determine the irreducible components of Igusa varieties for Shimura varieties of Hodge type under a mild condition and use that to compute the irreducible components of central leaves. In particular, we show that a strong version of the…

We show that the supersymmetric nonlinear Schr\"odinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two boson hierarchy through a field…

The relationships between port-Hamiltonian systems modeling and the notion of monotonicity are explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to maximal cyclically monotone relations, together…

We prove the integrability of the short pulse equation derived recently by Sch\"afer and Wayne from a hamiltonian point of view. We give its bi-hamiltonian structure and show how the recursion operator defined by the hamiltonian operators…

Recently Hirota and Kimura presented a new discretization of the Euler top with several remarkable properties. In particular this discretization shares with the original continuous system the feature that it is an algebraically completely…

In this paper we reinterpret the Poisson structure of the Hitchin-type system in cohomological terms. The principal ingredient of a new interpretation in the case of the Beauville system is the meromorphic cohomology of the spectral curve,…

The Hosotani mechanism in the closed-string theory with current algebra symmetry is described by the (old covariant) operator method. We compare the gauge symmetry breaking mechanism in a string theory which contains SU(2) symmetry…

We provide a complete classification of all the ways the Pais-Uhlenbeck osicllator might be embedded in two dimensional space. We discuss the Bi-Hamiltonian structures of this model, and examine how alternative Hamiltonian structures might…

In this work, we show that an autonomous dynamical system defined by a nonvanishing vector field on an orientable three-dimensional manifold is globally bi-Hamiltonian if and only if the first Chern class of the normal bundle of the given…

We study bi-Hamiltonian systems of hydrodynamic type with non-singular (semisimple) non-local bi-Hamiltonian structures and prove that such systems of hydrodynamic type are diagonalizable. Moreover, we prove that for an arbitrary…

The new generalized Harry Dym equation, recently introduced by Z. Popowicz in Phys. Lett. A 317, 260--264 (2003), is transformed into the Hirota--Satsuma system of coupled KdV equations.

We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with…

In this paper, we almost completely solve the existence of an almost resolvable cycle system with odd cycle length. We also use almost resolvable cycle systems as well as other combinatorial structures to give some new solutions to the…

Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale…

We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…

We propose one possible generalization of the KP hierarchy, which possesses multi bi--hamiltonian structures, and can be viewed as several KP hierarchies coupled together.

We propose a simple construction of the non-Hamiltonian dynamical systems possessing an invariant measure. These non-Hamiltonian systems are deformations of the Hamiltonian systems associated with trivial deformations of the canonical…

The purpose of this work is to propose a mixed Hodge structure over a CR manifold. As you know, for a CR manifold, Kohn-Rossi cohomology is naturally introduced. However, the relation between Kohn-Rossi cohomology and De Rham cohomology is…

This is a survey article, from the viewpoint of the completeness of the Marsden- Weinstein reduction, to introduce briefly some recent developments of the symmetric reductions and Hamilton-Jacobi theory of the regular controlled Hamiltonian…