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Related papers: A fifth-order bi-Hamiltonian system

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We generalize the Hamilton-Jacobi formulation for higher order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraint structure present in such systems.

High Energy Physics - Theory · Physics 2007-05-23 B. M. Pimentel , R. G. Teixeira

We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, Camassa-Holm equation, and…

Differential Geometry · Mathematics 2009-10-04 Paul Kersten , Iosif Krasil'shchik , Alexander Verbovetsky , Raffaele Vitolo

High order energy-preserving methods for Hamiltonian systems are presented. For this aim, an energy-preserving condition of continuous stage Runge--Kutta methods is proved. Order conditions are simplified and parallelizable conditions are…

Numerical Analysis · Mathematics 2016-11-08 Yuto Miyatake , John C. Butcher

We reduced the problem of constructing bi-Hamiltonian structure in three dimensions to the solution of a Riccati equation in moving coordinates of Serret-Frenet frame. We then show that either the linearly independent solutions of the…

Mathematical Physics · Physics 2007-12-03 E. Abadoglu , H. Gumral

We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems…

Mathematical Physics · Physics 2015-06-11 Jean-Francois Desilets , Pavel Winternitz , Ismet Yurdusen

A condition of reduction of multidimensional wave equations to the two-dimensional equation is studied, and the necessary conditions of compatibility and exact solutions of the resulting d'Alembert-Hamilton system are obtained.

Mathematical Physics · Physics 2007-05-23 W. I. Fushchych , I. A. Yehorchenko

In this paper we present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques proposed earlier by the authors of this paper, with a classical…

Numerical Analysis · Mathematics 2024-08-08 Firas Dhaouadi , Michael Dumbser , Sergey Gavrilyuk

The general method of the cojmplex supersymmetrization (supercomplexifications) of the soliton equations with the odd (bi) hamiltoninan structure is established. New version of the supercomplexified Kadomtsev-Petvishvili hierarchy is given.…

Exactly Solvable and Integrable Systems · Physics 2016-08-15 Ziemowit Popowicz

We present {\it symmetric Hamiltonians} for the degenerate Garnier systems in two variables. For these symmetric Hamiltonians, we make the symmetry and holomorphy conditions, and we also make a generalization of these systems involving…

Algebraic Geometry · Mathematics 2011-02-15 Yusuke Sasano

We investigate the multiplicity of solutions for a Hamiltonian system coupling two systems associated with mixed boundary conditions. Corresponding to the first system, we impose periodic boundary conditions and assume the twist assumption…

Classical Analysis and ODEs · Mathematics 2024-12-10 Wahid Ullah

We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in geosciences or medical applications. We propose a port-Hamiltonian formulation of the system…

Dynamical Systems · Mathematics 2021-04-13 Robert Altmann , Volker Mehrmann , Benjamin Unger

In this paper we construct the two component supersymmetric generalized Harry Dym equation which is integrable and study various properties of this model in the bosonic limit. In particular, in the bosonic limit we obtain a new integrable…

Exactly Solvable and Integrable Systems · Physics 2008-11-26 Ashok Das , Ziemowit Popowicz

In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradient-cutting algorithm which is extended from…

Optimization and Control · Mathematics 2015-10-28 Dang Van Hieu

We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…

Numerical Analysis · Mathematics 2021-06-30 Sana Keita , Abdelaziz Beljadid , Yves Bourgault

This study introduces standard Cliffordian Kaehler analogue of Hamiltonian mechanic systems. In the end, the some results related to standard Cliffordian Kaehler dynamical systems are also discussed.

Mathematical Physics · Physics 2009-02-24 Mehmet Tekkoyun

In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time…

Optimization and Control · Mathematics 2025-06-26 Kamal Fenza , Moussa Labbadi , Mohamed Ouzahra

We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of…

Exactly Solvable and Integrable Systems · Physics 2009-11-11 F. Neyzi , Y. Nutku , M. B. Sheftel

In this paper we construct a new completely integrable system. This system is an instance of a master system of differential equations in $5$ unknowns having $3$ quartics constants of motion.We find via the Painlev\'e analysis the principal…

Algebraic Geometry · Mathematics 2014-01-16 A. Lesfari

We investigate the reductions of dispersionless Harry Dym hierarchy to systems of finitely many partial differential equations. These equations must satisfy the compatibility condition and they are diagonalizable and semi-Hamiltonian. By…

Exactly Solvable and Integrable Systems · Physics 2009-11-11 Jen-Hsu Chang

Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…

Quantum Physics · Physics 2008-11-26 A. Ganguly , L. M. Nieto