Related papers: Lagrangian Approach to Dispersionless KdV Hierarch…
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and…
We studied the constrained Hamiltonian formulation of a supersymmetric Korteweg-de Vries (KdV) equation, which is observed to be a constrained system similar to its classical version. We found a nontrivial Lagrangian description, where we…
A hybrid framework is developed that highlights and unifies the most important aspects of the Noether correspondence between symmetries and conserved integrals in Lagrangian and Hamiltonian mechanics. Several main results are shown: (1) a…
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the…
For difference variational problems on lattice, this paper presents a relation between divergence variational symmetries and conservation laws for the associated Euler-Lagrange system provided by Noether's theorem. This hence inspires us to…
A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries are obtained and used to derive conservation laws via…
Noether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped harmonic oscillator problem with respect to…
We analyse the complex-valued Klein-Gordon Equation from an integrability perspective by the implementation of the Lie Theory of Continuous Groups, where this equation is governed by power-law nonlinearity. We write the equations in terms…
The dynamics of the highly nonlinear fifth order $KdV$-type equation is discussed in the framework of the Lagrangian and Hamiltonian formalisms. The symmetries of the Lagrangian produce three commuting conserved quantities that are found to…
Using methods of math.DG/0304245 and [I.S.Krasil'shchik and P.H.M.Kersten, Symmetries and recursion operators for classical and supersymmetric differential equations, Kluwer, 2000], we accomplish an extensive study of the N=1 supersymmetric…
Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…
We investigate the dispersionless Veselov-Novikov (dVN) equation based on the framework of dispersionless two-component BKP hierarchy. Symmetry constraints for real dVN system are considered. It is shown that under symmetry reductions, the…
We introduce the concept of Hamiltonian potential variables to map Hamiltonian operators into symplectic operators in a dual space. This generalises the classical trick of switching to a potential variable to obtain a Lagrangian density for…
This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws…
We obtain a covariant decomposition of the motion of a relativistic charged particle into parallel motion and perpendicular gyration, and transform to guiding-center coordinates using Lie transforms. The natural guiding-center Poisson…
We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
We propose a hierarchy of nonlinearly dispersive generalized Korteweg--de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. It is shown that two…
A supersymmetric breaking procedure for $N=1$ Super KdV, using a Clifford algebra, is implemented. Dirac's method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting…
The relation between the infinite-dimensional 3-algebras and the dispersionless KdV hierarchy is investigated. Based on the infinite-dimensional 3-algebras, we derive two compatible Nambu Hamiltonian structures. Then the dispersionless KdV…