Similarity solutions of the deformed Maxwell-Bloch system

The authors have found similarity reductions for the deformed Maxwell-Bloch system to the fifth and second Painleve equations. Asymptotics of the solutions of these equations, which are relevant to two-level atomic systems with pumping, have also been derived.

[1]  S. Burtsev.  The Maxwell-Bloch system with pumping and the fifth Painlevé equation , 1993 .

[2]  P. Deift,et al.  A steepest descent method for oscillatory Riemann-Hilbert problems , 1992, math/9201261.

[3]  A. Rybin.  Application of the Darboux transformation to inverse problems with variable spectral parameters , 1991 .

[4]  V. Korepin,et al.  Temperature correlators of the impenetrable Bose gas as an integrable system , 1990 .

[5]  M. Kruskal,et al.  New similarity reductions of the Boussinesq equation , 1989 .

[6]  A. V. Kitaev,et al.  THE METHOD OF ISOMONODROMY DEFORMATIONS AND THE ASYMPTOTICS OF SOLUTIONS OF THE “COMPLETE” THIRD PAINLEVÉ EQUATION , 1989 .

[7]  Athanassios S. Fokas,et al.  A method of linearization for Painleve´ equations: Painleve´ IV, V , 1988 .

[8]  Vladimir E. Zakharov,et al.  Inverse scattering method with variable spectral parameter , 1987 .

[9]  Alexander Its,et al.  Isomonodromic Deformation Method in the Theory of Painleve Equations , 1986 .

[10]  B. McCoy,et al.  Connection formulae for Painleve´ V functions , 1986 .

[11]  I. Gabitov,et al.  Maxwell-Bloch equation and the inverse scattering method , 1985 .

[12]  Gernot Neugebauer,et al.  Einstein-Maxwell solitons , 1983 .

[13]  Michio Jimbo,et al.  Monodromy Problem and the Boundary Condition for Some Painlevé Equations , 1982 .

[14]  M. Jimbo,et al.  Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II , 1981 .

[15]  A. Newell,et al.  Monodromy- and spectrum-preserving deformations I , 1980 .

[16]  G. Lamb.  Elements of soliton theory , 1980 .

[17]  D. Kaup.  Coherent pulse propagation: A comparison of the complete solution with the McCall-Hahn theory and others , 1977 .

[18]  F. Bureau.  Équations différentielles du second ordre enY et du second degré enŸ dont l'intégrale générale est à points critiques fixes , 1971 .