Integrability aspects and soliton solutions for the inhomogeneous reduced Maxwell-Bloch system in nonlinear optics with symbolic computation

DOI10.1016/j.cnsns.2014.07.018zbMath1337.78011OpenAlexW2094592371MaRDI QIDQ907697

Hui-Qin Hao, Jian-Wen Zhang

Publication date: 26 January 2016

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2014.07.018

zbMATH Keywords

soliton solutionsDarboux transformationintegrability aspectsasymptotic analysis methodinhomogeneous reduced Maxwell-Bloch system

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Asymptotic expansions of solutions to PDEs (35C20) Lasers, masers, optical bistability, nonlinear optics (78A60) Asymptotic analysis in optics and electromagnetic theory (78M35)

Related Items (4)

The canonical AB system: conservation laws and soliton solutions ⋮ Bilinear Forms and Soliton Solutions for the Reduced Maxwell-Bloch Equations with Variable Coefficients in Nonlinear Optics ⋮ Darboux transformation and soliton solutions of the \((2 + 1)\)-dimensional derivative nonlinear Schrödinger hierarchy ⋮ Conservation laws, solitons, Breather and rogue waves for the (2+1)-dimensional variable-coefficient Nizhnik-Novikov-Veselov system in an inhomogeneous medium

Cites Work

• Unnamed Item
• Analytic localized solitonic excitations for the \((2+1)\)-dimensional variable-coefficient breaking soliton model in fluids and plasmas
• Generalized Cauchy matrix approach for lattice KP-type equations
• Direct linearization of the nonisospectral Kadomtsev-Petviashvili equation
• Approximate solutions of Maxwell Bloch equations and possible Lotka-Volterra type behavior
• Approximate conservation laws of perturbed partial differential equations
• The double Wronskian solutions of a non-isospectral Kadomtsev-Petviashvili equation
• Variational principles and conservation laws to the Burridge-Knopoff equation
• Conservation laws of multidimensional diffusion-convection equations
• Potential symmetries and associated conservation laws with application to wave equations
• Nonlinear optical waves
• Soliton solutions for the reduced Maxwell-Bloch system in nonlinear optics via the \(N\)-fold Darboux transformation
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• Nonlinear-Evolution Equations of Physical Significance
• Darboux transformation and new periodic wave solutions of generalized derivative nonlinear Schrödinger equation
• The Painleve test, Backlund transformation and solutions of the reduced Maxwell-Bloch equations
• Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation
• N-fold Darboux transformation and soliton solutions for a nonlinear Dirac system

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