Results 1 - 10 of 6514
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[en] We propose a method of calculating the operator densities hsub(n) n=0,1, ... of the conservation laws for the quantum nonlinear Schroedinger equation. It follows from the method that hsub(n) are, polynomials in fields and their derivatives and in the coupling constant. The densities hsub(n) <= 4 are explicitly calculated. Comparison with the integral densities bsub(n) n=0, 1, ... for the classical monlinear Schroedinger equation shows that the correspondence between hsub(n) and bsub(n) breaks down after n=3
[en] We describe an approach to investigate the Hamiltonian structures of discrete soliton systems, which is deduced from the relation between the conservation laws and the Hamiltonian structures. As to its applications, the Toda lattice, the Blaszak-Marciniak lattice and the Blaszak-Marciniak (II) are discussed.
[en] We consider a four-velocity discrete and unidimensional Boltzmann model. The mass, momentum and energy conservation laws being satisfied we can define a temperature. We report the exact positive solutions which have been found: periodic in the space and propagating or not when the time is growing, shock waves similarity solutions and (1 + 1)-dimensional solutions
[fr]Nous considerons un modele de Boltzmann unidimensionnel a quatre vitesses. Ce modele, satisfaisant trois lois de conservation de la masse du moment et de l'energie, permet de definir une temperature. Pour ce modele des solutions exactes positives existent: solutions periodiques dans l'espace se propageant ou non lorsque le temps varie, solutions de similarite d'ondes de choc et solutions a 1 + 1 dimensions
[en] A new conserved quantity is investigated by utilizing the definition and discriminant equation of Mei symmetry of Tzénoff equations for nonholonomic systems. In addition, the expression of this conserved quantity, and the determining condition induced new conserved quantity are also presented
[en] Until the 1970's all theories of elementary particles assumed the absolute validity of the law of baryon conservation, i.e., that the number of baryons plus antibaryons is constant in any interaction. The idea the baryons are absolutely conserved was first put forth by Weyl and then by Stuckelberg and Wigner. In those early days the term baryon conservation meant nucleon conservation. Today, however, we know of more than sixty types of baryons. This paper reports that, thus there are many systems in which it is possible to look for baryon nonconservation
[en] For a Birkhoffian system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results
[en] We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman et al. [J. Math. Phys. 47, 113505 (2006)]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings, and general foliated systems of differential equations. An example illustrating possible applications of these results is given. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws
[en] The symmetries and non-Noether conservation laws of Birkhoffian system with unilateral constraints are studied. The differential equations of motion of the system are established, and the criterions of Noether symmetry, Lie symmetry and Mei symmetry of the system are given. Two types of new conservation laws, called the Hojman conservation law and the Mei conservation law respectively, are obtained, and the intrinsic relations among the symmetries and the new conservation laws are researched. At the end of the paper, an example is given to illustrate the application of the results.
[en] We study the symmetries of the generalized lagrangian of two point masses, in the post-post newtonian approximation of General Relativity. We deduce, via Noether's theorem, conservation laws for energy, linear and angular momentum, as well as a generalisation of the center-of-mass theorem
[fr]On etudie les symetries du lagrangien generalise de deux masses ponctuelles, a l'approximation post-post newtonienne de la Relativite generale. On en deduit, grace au theoreme de Noether, les lois de conservation de l'energie, de l'impulsion et du moment cinetique du systeme, ainsi que la generalisation du theoreme du centre de masse