相关论文: Symmetries of Helmholtz forms and globally variati…
An inhomogeneous linear differential equation Ly=f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in…
In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian $L(x(t)$, where $_a^cD_t^\alpha x(t))$ and $0<\alpha< 1$, such that the following…
We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal…
The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations…
We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number…
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…
We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional…
Duality is one of the oldest known symmetries of Maxwell equations. In recent years the significance of duality symmetry has been recognized in superstrings and high energy physics and there has been a renewed interest on the question of…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the…
Based on the Euler-Lagrange cohomology groups $H_{EL}^{(2k-1)}({\cal M}^{2n}) (1 \leqslant k\leqslant n)$ on symplectic manifold $({\cal M}^{2n}, \omega)$, their properties and a kind of classification of vector fields on the manifold, we…
In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing…
A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of discontinuities (including shocks) is presented in the framework of an exact Clebsch type representation…
The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…
We discuss a general definition of directional derivative of any tensor flow field and its practical applications in physics. It is shown that both Lagrangian and Eulerian descriptions as complementary types of flow field specifications…
In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function $H$ with the delta integral of a vector valued field $f$, i.e., of the form…
We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
We study a multi-objective variational problem of Herglotz' type with cooperative linear coupling. We established the associated Euler-Lagrange equations and the characteristic system for cooperative weakly coupled systems of…