Journal•ISSN: 0040-5779
Theoretical and Mathematical Physics
Russian Academy of Sciences
About: Theoretical and Mathematical Physics is an academic journal published by Russian Academy of Sciences. The journal publishes majorly in the area(s): Nonlinear system & Hamiltonian (quantum mechanics). It has an ISSN identifier of 0040-5779. Over the lifetime, 7888 publications have been published receiving 77955 citations. The journal is also known as: Theoretical and mathematical physics (New York. Print) & Theoretical and mathematical physics (New York. Internet).
Topics: Nonlinear system, Hamiltonian (quantum mechanics), Quantum field theory, Integrable system, Scattering
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1,005 citations
TL;DR: In this article, additional symmetries in two-dimensional conformal field theory generated by spin s = 1/2, 1,...,3 currents were investigated and the generators of the symmetry form associative algebras with quadratic determining relations.
Abstract: This paper investigates additional symmetries in two-dimensional conformal field theory generated by spin s = 1/2, 1,...,3 currents. For spins s = 5/2 and s = 3, the generators of the symmetry form associative algebras with quadratic determining relations. ''Minimal models'' of conforma field theory with such additional symmetries are considered. The space of local fields occurring in a conformal field theory with additional symmetry corresponds to a certain (in general, reducible) representation of the corresponding algebra of the symmetry.
910 citations
866 citations
TL;DR: In this article, a new partial differential equation, of a similar form to the Camassa-Holm shallow water wave equation, was obtained by Degasperis and Procesi using the method of asymptotic integrability.
Abstract: We consider a new partial differential equation, of a similar form to the Camassa-Holm shallow water wave equation, which was recently obtained by Degasperis and Procesi using the method of asymptotic integrability. We prove the exact integrability of the new equation by constructing its Lax pair, and we explain its connection with a negative flow in the Kaup-Kupershmidt hierarchy via a reciprocal transformation. The infinite sequence of conserved quantities is derived together with a proposed bi-Hamiltonian structure. The equation admits exact solutions in the form of a superposition of multi-peakons, and we describe the integrable finite-dimensional peakon dynamics and compare it with the analogous results for Camassa-Holm peakons.
727 citations
TL;DR: In this paper, a simple exact analytic solution of the nonlinear Schroedinger equation is found in the class of periodic solutions, which describes the time evolution of a wave with constant amplitude on which a small periodic perturbation is superimposed.
Abstract: A very simple exact analytic solution of the nonlinear Schroedinger equation is found in the class of periodic solutions. It describes the time evolution of a wave with constant amplitude on which a small periodic perturbation is superimposed. Expressions are obtained for the evolution of the spectrum of this solution, and these expressions are analyzed qualitatively. It is shown that there exists a certain class of periodic solutions for which the real and imaginary parts are linearly related, and an example of a one-parameter family of such solutions is given.
723 citations