• Article  

      Bogoyavlensky-Toda systems of type DN 

      Damianou, Pantelis A.; Kouzaris, S. P. (2003)
      In this paper we confirm a conjecture of Flaschka which relates the hierarchy of Poisson brackets and master symmetries for the Bogoyavlesky-Toda systems of type Dn with fundamental invariants of the corresponding Lie ...
    • Article  

      Bogoyavlensky-Volterra and Birkhoff integrable systems 

      Damianou, Pantelis A.; Kouzaris, S. P. (2004)
      In this paper we examine an interesting connection between the generalized Volterra lattices of Bogoyavlensky and a special case of an integrable system defined by Sklyanin. The Sklyanin system happens to be one of the ...
    • Article  

      Classification of noether symmetries for Lagrangians with three degrees of freedom 

      Damianou, Pantelis A.; Sophocleous, Christodoulos (2004)
      The noether symmetries of the Euler-Lagrange equations for a Hamiltonian system with three degrees were classified. All groups were classified that appeared as symmetries of a general Hamiltonians system of n degrees of ...
    • Conference Object  

      A computer simulation scenario analysis approach as a decision support tool for transportation systems planning 

      Papageorgiou, George; Damianou, Pantelis A.; Pitsillides, Andreas; Aphamis, Thrasos; Ioannou, Petros A. (2007)
      As the level of traffic congestion rises and the complexity of traffic networks increases, the development of effective transportation strategies becomes the most challenging task for every transport authority. Meanwhile, ...
    • Conference Object  

      A construction of generalized Lotka–volterra systems connected with Sln.(C) 

      Charalambides, Stelios A.; Damianou, Pantelis A.; Evripidou, Charalambos A. (Springer New York LLC, 2014)
      We construct a large family of Hamiltonian systems which are connected with root systems of complex simple Lie algebras. These systems are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic ...
    • Article  

      Darboux polynomials for lotkavolterra systems in three dimensions 

      Christodoulides, Y. T.; Damianou, Pantelis A. (2009)
      We consider LotkaVolterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for ...
    • Article  

      From the Toda lattice to the Volterra lattice and back 

      Damianou, Pantelis A.; Fernandez, R. L. (2002)
      We discuss the relationship between the multiple Hamiltonian structures of the generalized Toda lattices and that of the generalized Volterra lattice.
    • Article  

      Generalized Lotka - Volterra systems connected with simple Lie algebras 

      Charalambides, Stelios A.; Damianou, Pantelis A.; Evripidou, Charalambos A. (2015)
      We devise a new method for producing Hamiltonian systems by constructing the corresponding Lax pairs. This is achieved by considering a larger subset of the positive roots than the simple roots of the root system of a ...
    • Article  

      Generalized Lotka—Volterra systems connected with simple Lie algebras 

      Charalambides, Stelios A.; Damianou, Pantelis A.; Evripidou, Charalambos A. (2015)
    • Article  

      A gentle (without Chopping) approach to the full Kostant-toda lattice 

      Damianou, Pantelis A.; Magri, F. (2005)
      In this paper we propose a new algorithm for obtaining the rational integrals of the full Kostant-Toda lattice. This new approach is based on a reduction of a bi-Hamiltonian system on gl(n, R). This system was obtained by ...
    • Article  

      Integrable hierarchies and the modular class 

      Damianou, Pantelis A.; Fernandes, R. L. (2008)
      It is well-known that the Poisson-Nijenhuis manifolds, introduced by Kosmann-Schwarzbach and Magri form the appropriate setting for studying many classical integrable hierarchies. In order to define the hierarchy, one ...
    • Article  

      Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems 

      Damianou, Pantelis A.; Evripidou, Charalambos A.; Kassotakis, P.; Vanhaecke, P. (2017)
      Given a constant skew-symmetric matrix A, it is a difficult open problem whether the associated Lotka-Volterra system is integrable or not.We solve this problem in a special case when A is a Toeplitz matrix where all ...
    • Article  

      Intermediate Toda systems 

      Damianou, Pantelis A.; Sabourin, H.; Vanhaecke, P. (2015)
      We construct a large family of Hamiltonian systems which interpolate between the classical Kostant-Toda lattice and the full Kostant-Toda lattice and we discuss their integrability. There is one such system for every ...
    • Article  

      Lax pairs, symmetries and recursion operators for Toda lattices 

      Damianou, Pantelis A. (1997)
      With the exception of some minor results and some conjectures, this paper is a survey of the finite nonperiodic Toda lattices and some of their generalizations. The areas investigated include Lax pairs, master symmetries, ...
    • Article  

      Looking for the integrating factor: The darboux approach 

      Christodoulides, Y. T.; Damianou, Pantelis A. (2014)
      We present a method for the solution of first-order ordinary differential equations based on a class of polynomials known as Darboux polynomials. Integrating factors, used to convert the equations in exact form, and constants ...
    • Article  

      Lotka-Volterra equations in three dimensions satisfying the Kowalevski-Painlevé property 

      Constandinides, Kyriacos; Damianou, Pantelis A. (2011)
      We examine a class of Lotka-Volterra equations in three dimensions which satisfy the Kowalevski-Painlevé property. We restrict our attention to Lotka-Volterra systems defined by a skew symmetric matrix. We obtain a complete ...
    • Article  

      Master symmetries and R-matrices for the Toda lattice 

      Damianou, Pantelis A. (1990)
      A hierarchy of vector fields (master symmetries) and homogeneous nonlinear Poisson structures associated with the Toda lattice are constructed and the various connections between them are investigated. These brackets may ...
    • Article  

      Modelling and simulation of transportation systems: A scenario planning approach 

      Papageorgiou, George; Damianou, Pantelis A.; Pitsillides, Andreas; Aphamis, Thrasos; Charalambous, Demetris; Ioannou, Petros A. (2009)
      It is increasingly realized that building more roads does not solve the traffic congestion problem but actually makes it worse. Instead of adding capacity to our roads there should be an effort to find ways in order to ...
    • Article  

      The modular hierarchy of the Toda lattice 

      Agrotis, Maria A.; Damianou, Pantelis A. (2007)
      The modular vector field plays an important role in the theory of Poisson manifolds and is intimately connected with the Poisson cohomology of the space. In this paper we investigate its significance in the theory of ...
    • Article  

      Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices 

      Damianou, Pantelis A. (2004)
      This paper is mainly a review of the multi-Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include ...