The Painleve test, Backlund transformation and solutions of the reduced Maxwell-Bloch equations
- 11 March 1986
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 19 (4) , 479-484
- https://doi.org/10.1088/0305-4470/19/4/009
Abstract
The Painleve property for partial differential equations (PDES) proposed by Weiss et al. (1983) is studied for a system of PDES, namely the reduced Maxwell-Bloch (RMB) equations. The RMB equations describe the propagation of short optical pulses through dielectric materials with a resonant non-degenerate transition. The author demonstrates that the RMB system passes the Painleve test, and constructs a Backlund transformation and solutions of the RMB equations.Keywords
This publication has 16 references indexed in Scilit:
- Sinh-Gordon equation, Painlevé property and Bäcklund transformationPhysica A: Statistical Mechanics and its Applications, 1985
- Nonlinear lattice equation in (1+1) dimensions in continuum approximation, Painlevé test and solutionsSolid State Communications, 1985
- Painleve property and multicomponent isospectral deformation equationsPhysics Letters A, 1983
- Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimesJournal of Mathematical Physics, 1982
- Integrable Hamiltonian systems and the Painlevé propertyPhysical Review A, 1982
- A connection between nonlinear evolution equations and ordinary differential equations of P-type. IJournal of Mathematical Physics, 1980
- Solitons in Laser PhysicsPhysica Scripta, 1979
- Exact Multisoliton Solution of the Reduced Maxwell-Bloch Equations of Non-linear OpticsIMA Journal of Applied Mathematics, 1974
- AnN-soliton solution of a nonlinear optics equation derived by a general inverse methodLettere al Nuovo Cimento (1971-1985), 1973
- Solitons in nonlinear optics. I. A more accurate description of the 2π pulse in self-induced transparencyJournal of Physics A: Mathematical, Nuclear and General, 1973