Related papers: Integrable discretization of hodograph-type system…

We consider the continuous and discrete-time Hamilton's variational principle on phase space, and characterize the exact discrete Hamiltonian which provides an exact correspondence between discrete and continuous Hamiltonian mechanics. The…

This paper focuses on the numerical approximation of the linearized shallow water equations using hybridizable discontinuous Galerkin (HDG) methods, leveraging the Hamiltonian structure of the evolution system. First, we propose an…

This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…

Following the discrete embedding formalism, we give a new derivation of the mid-point variational integrators as developed by J.M. Wendlandt and J.E. Marsden by defining an adapted order two discrete differential and integral calculus. This…

As a generalization and extension of our previous paper [Escobar-Ruiz and Azuaje, J. Phys. A: Math. Theor. 57, 105202 (2024)], in this work, the notions of particular integral and particular integrability in classical mechanics are extended…

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation, and the short pulse equation. They are related to the…

This paper provides a first contribution to port-Hamiltonian modeling of district heating networks. By introducing a model hierarchy of flow equations on the network, this work aims at a thermodynamically consistent port-Hamiltonian…

We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.

Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time…

In this paper we consider non-diagonalisable hydrodynamic type systems integrable by the Extended Hodograph Method. We restrict our consideration to non-diagonalisable hydrodynamic reductions of the Mikhalev equation. We show that families…

This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element…

We consider the special type of the field-theoretical Symplectic structures called weakly nonlocal. The structures of this type are in particular very common for the integrable systems like KdV or NLS. We introduce here the special class of…

In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…

A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…

In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.

The Whitham approach is a well-studied method to describe non-linear integrable systems. Although approximate in nature, its results may predict rather accurately the time evolution of such systems in many situations given initial…

We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the…

This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…

In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…