Inverse Scattering Transform and Soliton Classification of Higher-Order Nonlinear Schrödinger-Maxwell-Bloch Equations
Zhiqiang Li, Shou‐Fu Tian, Wei‐Qi Peng, Jin‐Jie Yang
Abstract
We investigate higher-order nonlinear Schrödinger-Maxwell-Bloch equations using the Riemann-Hilbert method. We perform a spectral analysis of the Lax pair and construct a Riemann-Hilbert problem according to the spectral analysis. As a result, we obtain three types of multisoliton solutions. Based on the analytic solution and with a choice of corresponding parameter values, we obtain solutions of the breather type and a bell-shaped solution and find an interesting phenomenon of the collision of two soliton solutions. We hope that these results can be useful in modeling the wave propagation of a nonlinear optical field in an erbium-doped fiber medium.
Topics & Concepts
Inverse scattering problemLax pairBreatherSolitonInverse scattering transformNonlinear systemRiemann hypothesisMathematical analysisPhysicsMathematicsMathematical physicsInverse problemQuantum mechanicsNonlinear Waves and SolitonsNonlinear Photonic SystemsAdvanced Fiber Laser Technologies