Conservation laws for polynomial quantum Hamiltonians

A construction method for the conservation laws for a broad class of polynomial quantum Hamiltonians is proposed. Also the classification of irreducible representations of some nonlinear commutation relation is given.     

Conservation laws of the generalized short pulse equation

We show that the generalized short pulse equation is nonlinearly self-adjoint with differential substitution.Moreover,any adjoint symmetry is a differential substitution of nonlinear self-adjointness,and vice versa.Consequently,the general conservation law formula is constructed and new conservation laws for some special cases are found.     

Conservation laws and symmetries of generalized sine-Gordon equations

We study some systems of non-linear PDE's (Eqs. 1.1 below) which can be regarded either as generalizations of the sine-Gordon equation or as two-dimensional versions of the Toda lattice equations. We show that these systems have an infinite number of non-trivial conservation laws and an infinite number of symmetries. The second result is deduced from the first by a variant of the Hamiltonian formalism for evolution equations. We also consider some specializations of the systems.     

Conservation laws of the generalized nonlocal nonlinear Schrodinger equation

The derivations of several conservation laws of the generalized nonlocal nonlinear Schr?dinger equation are presented. These invariants are the number of particles, the momentum, the angular momentum and the Hamiltonian in the quantum mechanical analogy. The Lagrangian is also presented.     

Conservation laws in acoustics

The method earlier proposed by the author for obtaining a complete set of conservation laws is applied to a number of simple acoustic problems. Some of the conservation laws presented are derived for the first time. Special attention is given to the physical interpretation of the results.     

Conservation laws in general relativity

In recent years an increased interest in General Relativity Theory (GRT) has been apparent among theoretical physicists, mathematicians, astronomers and geophysicists. At the same time, the necessity of rinding a final and generally satisfactory solution of a very important problem, namely that of conservation laws, has become topical. Surprising difficulties have been encountered in the attempt to transfer these concepts to General Relativity Theory. In the course of a few years a comprehensive literature has resulted and now the time is ripe for a thorough summary of the results attained so far.The authors would like to thank Dr. P. Burcev from the Dept of Theoretical Physics, J. E. Purkyn University in Brno, and Dr. K. Kucha from the Dept. of Theoretical Physics, Charles University in Prague, for their permanent interest in this work and for valuable discussions.     

Conservation laws in Bimetric gravitation theories

In the bimetric theory of gravitation with a flat-space background metric conservation laws for energy and momentum are considered in several different forms. In the bimetric theory with a constant-curvature background metric a previous error in the energy-momentum relation is corrected.     

Conservation laws in asymptotically separable quantum mechanics

A notion of chronological disorder is introduced to explain the physical reason why many familiar conservation laws should not be regarded as sacrosanct and valid for all times. Their disappearance as absolute laws in an asymptotically separable theory is a desirable feature, rather than a difficulty, of the theory.     

Conservation laws in a directed sandpile model

We derive a complete set of conservation laws for a directed sandpile model originally studied by Dhar and Ramaswamy, and discuss the rather minimal effect of these laws on the dynamics of avalanches.     

Conservation laws and residual interaction in nuclei

Zeitschrift für Physik A Hadrons and nuclei - We discuss relations between single-particle energies and parameters of the residual interaction in nuclei, which follow from galilean and gauge...     

Conservation laws of free Klein Gordon fields

It is proved that the free Klein Gordon fields of spatial dimension 2 have no conservation laws expressible by differential polynomials with constant coefficients other than those found by Kibble [5].Partially supported by Sakkokai Foundation and the National Science Foundation.     

Conservation laws in stochastic deposition-evaporation models in one dimension

An infinite number of conservation laws is identified for a stochastic model of deposition and evaporation of trimers on a linear chain. These laws can be encoded into a single nonlocal invariant, the irreducible string, which uniquely lables an exponentially large number of kinetically disconnected sectors of phase space. This enables the number and sizes of sectors to be determined. The effects of conservation laws on some thermodynamic properties are studied.     

Conservation laws in General Relativity in the Vierbein formalism

Conservation laws for dynamical systems in Riemannian space-time in the Vierbein formalism are deduced from the existence of motions in the space-time. The result is applied to Dirac's equation in General Relativity. Research partially supported by the National Research Council of Canada.