相关论文: Linearisation of Universal Field Equations

The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…

The relationship between the Hamiltonian and Lagrangean functions in analytical mechanics is a type of duality. The two functions, while distinct, are both descriptive functions encoding the behavior of the same dynamical system. One…

One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to…

The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…

It is shown that the addition of a non-linear term to the Lagrangian of the electromagnetic field yields a fluid with an asymptotically super-negative equation of state, causing an accelerated expansion of the universe. Some general…

We demonstrate that interesting examples of Lagrangian multiforms appear naturally in the theory of multidimensional dispersionless integrable systems as (a) higher-order conservation laws of linearly degenerate PDEs in 3D, and (b) in the…

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single…

In a space of 4-dimensions, I will examine constrained variational problems in which the Lagrangian, and constraint scalar density, are concomitants of a (pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange…

We propose a new formulation of $f(R)$ gravity, dubbed scalarized $f(R)$ gravity, in which the Legendre transform is included as a dynamical term. This leads to a theory with second-order field equations that describes general relativity…

The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is presented. The paradigm example studied in this paper is the Euclidean scalar field with a…

We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence…

I review some open problems on the ever-growing field of non-equilibrium phase transitions, paying special attention to the formulation of such problems in terms of Langevin equations or, equivalently, field-theoretical descriptions, and…

A method for constructing general null Lagrangians and their higher harmonics is presented for dynamical systems with one degree of freedom. It is shown that these Lagrangians can be used to obtain non-standard Lagrangians, which give…

In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.

It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so--called ``Palatini formalism'', i.e., treating the metric and the connection as…

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are…

We update and detail the formulation of the duality-invariant systems of N interacting abelian gauge fields with N auxiliary bispinor fields added. In this setting, the self-duality amounts to U(N) invariance of the nonlinear interaction of…

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a…

In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…