Related papers: Continuum limits of pluri-Lagrangian systems
In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the…
Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the…
Anti-integrable limit is one of convenient and relatively simple methods for construction of chaotic hyperbolic invariant sets in Lagrangian, Hamiltonian and other dynamical systems. We discuss the most natural context of the method --…
This paper presents a Lagrangian approach to simulating multibody dynamics in a tensegrity framework with an ability to tackle holonomic constraint violations in an energy-preserving scheme. Governing equations are described using…
We will give a short introduction to discrete or lattice soliton equations, with the particular example of the Korteweg-de Vries as illustration. We will discuss briefly how B\"acklund transformations lead to equations that can be…
A detailed program is proposed in the Lagrangian formalism to investigate the dynamical behavior of a theory with singular Lagrangian. This program goes on, at different levels, parallel to the Hamiltonian analysis. In particular, we…
Laser-induced-continuum-structure(LICS) allows for coherent control techniques to be applied in a Raman type system with intermediate continuum state. To this end the standard LICS problem treats two bound states coupled to one or more…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics-informed neural network and deep Ritz methods, we propose…
We address the interplay between local and global symmetries by analyzing the continuum limit of two-dimensional multicomponent scalar lattice gauge theories, endowed by non-Abelian local and global invariance. These theories are…
We present a quasi-integrable two-dimensional lattice equation: i.e., a partial difference equation which satisfies a criterion of integrability, singularity confinement, although it has a chaotic aspect in the sense that the degrees of its…
One dimensional nonlinear lattices with harmonic long range interaction potentials (LRIP) having an inverse power kernel type, are studied. For the nearest neighbour nonlinear interaction we consider the anharmonic potential of the…
The paper is focused on the dynamic homogenization of lattice-like materials with lumped mass at the nodes to obtain energetically consistent models providing accurate descriptions of the acoustic behavior of the discrete system. The…
This study proposes and analyses a novel higher-order, structure preserving discretization method for inviscid barotropic flows from a Lagrangian perspective. The method is built on a multisymplectic variational principle discretized over a…
In this work, we present another example of the Lagrangian 1-form structure for the hy- perbolic Calogero-Moser system both in discrete-time level and continuous-time level. The discrete-time hyperbolic Calogero-Moser system is obtained by…
Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium…
In a previous paper by one of the authors, a Lagrangian 3-form structure was established for a generalised Darboux system, originally describing orthogonal curvilinear coordinate systems, which encodes the Kadomtsev-Petviashvili (KP)…
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…
We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete…