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Time evolution of infinitely many particles; an existence theorem
413
Nonlinear science abstracts
fields. Other examples of coupling by the gauge group are given, application to the Maxwell-Schr~dinger equation. JOURNAL: not given
including an
78
(P1,T7) TIME EVOLUTION OF INFINITELY MANY PARTICLES ; AN EXISTENCE THEOREM. P. Calderoni, Istituto Matematco, Universita di Roma and S. Caprino, Istituto Matematico, Universita di Camerino 62032 Camerino (MC) Italy. Please send all correspondence to S. Caprino. R3, The paper deals with systems of infinitely many particles in acted on by a two body, short range potential and an external potential, depending on the position of the particles. It is proven the existence of dynamics for a set of initial configurations, which is of measure one with respect to the Gibbs measures induced by a suitable family of Hamiltonians. JOURNAL: to appear - Journal of Statistical Physics, vol. 28, No. 4, 1982 79
(P6,T7) COMMENTS ON: THE MAXWELL-VLASOV EQUATIONS AS A CONTINUOUS HAMILTONIAN SYSTEM. Alan Weinstein, Department of Mathematics, University of California, Berkeley, CA 94720, USA; Philip J. Morrison, Plasma Physics Laboratory, Princeton University, Princeton, NJ 08544, USA. The Poisson structure previously introduced by Morrison for the Maxwell-Vlasov equations does not satisfy the Jacobi identity. The corrected Poisson structure has been found by Marsden and Weinstein. It is derived by standard constructions in symplectic geometry and therefore satisfies the Jacobi identity. JOURNAL: Physics Letters, Volume 86A, No. 4 (1981) 235. 80
(M2,T5) DISCONTINUOUS NONLINEAR EVOLUTION EQUATIONS; BROKEN CONSERVATION LAWS AND SOLITON TUNNELLING. F . M . Giusto, Scuola di Perfezionamento in Fisica dell Universita di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova; T. A. Minelli and A. Pascolini, Instituto di Fisica dell Universita di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova. An extension of the AKNS scheme and of the associated conservation laws to some nonlinear evolution equations with discontinuous coefficients is considered, in view also of the analysis of soliton fission and tunnelling and Bremsstrahlung production proceses. A nonlinear SchrSdinger equation with a potential-like term and a discontinuous KdV equations and their broken conservation laws are deduced. JOURNAL: not given 81
(PI,T2) EFFECTS OF ADDITIVE NOISE ON A NONLINEAR OSCILLATOR EXHIBITING PERIOD DOUBLING AND CHAOTIC BEHAVIOR. Jose Perez and Carson Jeffries, Materials and Molecular Research Division, Lawrence Berkeley Laboratory, and Department of Physics, University of California, Berkeley, CA 94720, USA. We report detailed effects of additive random noise on a driven nonlinear oscillator in the periodic, the chaotic, and the window regimes. We observe simultaneously the power spectral density, the probability density, and
Nonlinear science abstracts
fields. Other examples of coupling by the gauge group are given, application to the Maxwell-Schr~dinger equation. JOURNAL: not given
including an
78
(P1,T7) TIME EVOLUTION OF INFINITELY MANY PARTICLES ; AN EXISTENCE THEOREM. P. Calderoni, Istituto Matematco, Universita di Roma and S. Caprino, Istituto Matematico, Universita di Camerino 62032 Camerino (MC) Italy. Please send all correspondence to S. Caprino. R3, The paper deals with systems of infinitely many particles in acted on by a two body, short range potential and an external potential, depending on the position of the particles. It is proven the existence of dynamics for a set of initial configurations, which is of measure one with respect to the Gibbs measures induced by a suitable family of Hamiltonians. JOURNAL: to appear - Journal of Statistical Physics, vol. 28, No. 4, 1982 79
(P6,T7) COMMENTS ON: THE MAXWELL-VLASOV EQUATIONS AS A CONTINUOUS HAMILTONIAN SYSTEM. Alan Weinstein, Department of Mathematics, University of California, Berkeley, CA 94720, USA; Philip J. Morrison, Plasma Physics Laboratory, Princeton University, Princeton, NJ 08544, USA. The Poisson structure previously introduced by Morrison for the Maxwell-Vlasov equations does not satisfy the Jacobi identity. The corrected Poisson structure has been found by Marsden and Weinstein. It is derived by standard constructions in symplectic geometry and therefore satisfies the Jacobi identity. JOURNAL: Physics Letters, Volume 86A, No. 4 (1981) 235. 80
(M2,T5) DISCONTINUOUS NONLINEAR EVOLUTION EQUATIONS; BROKEN CONSERVATION LAWS AND SOLITON TUNNELLING. F . M . Giusto, Scuola di Perfezionamento in Fisica dell Universita di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova; T. A. Minelli and A. Pascolini, Instituto di Fisica dell Universita di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova. An extension of the AKNS scheme and of the associated conservation laws to some nonlinear evolution equations with discontinuous coefficients is considered, in view also of the analysis of soliton fission and tunnelling and Bremsstrahlung production proceses. A nonlinear SchrSdinger equation with a potential-like term and a discontinuous KdV equations and their broken conservation laws are deduced. JOURNAL: not given 81
(PI,T2) EFFECTS OF ADDITIVE NOISE ON A NONLINEAR OSCILLATOR EXHIBITING PERIOD DOUBLING AND CHAOTIC BEHAVIOR. Jose Perez and Carson Jeffries, Materials and Molecular Research Division, Lawrence Berkeley Laboratory, and Department of Physics, University of California, Berkeley, CA 94720, USA. We report detailed effects of additive random noise on a driven nonlinear oscillator in the periodic, the chaotic, and the window regimes. We observe simultaneously the power spectral density, the probability density, and