| Abstract: |
| We consider $N$-soliton solutions of the sharp-line Maxwell-Bloch system that may contain multiple degenerate soliton groups (DSGs). A DSG is a localized coherent nonlinear traveling-wave structure, consisting of inseparable solitons with identical velocities. Thus, DSGs are generalizations of single solitons (considered as $1$-DSGs), and constitute fundamental building blocks for the solutions of many integrable systems. We provide explicit formulae for an $N$-DSG and its center, and calculate the long-time asymptotics for such solutions. We also briefly discuss high-order soliton solutions, which can be regarded as generalizations of the $N$-soliton solutions. |
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