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<p>Newly shaped solitons and rogue waves on several periodic background in the reduced spin Hirota–Maxwell–Bloch (rsHMB) system are presented. First, various seed solutions of the rsHMB system are established, including constant solutions and four types of Jacobian elliptic function solutions. Then, by means of the nonlinearization of Lax pairs and the Darboux transformation (DT) method, the general expressions of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q(x, t)\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\eta (x, t)\)</EquationSource> </InlineEquation> are derived by corresponding several seed solutions including constant solutions, dn, cn, nd and sd solutions, respectively. N-shaped solitons, M-shaped solitons, W-shaped solitons, multi-peaked solitons as well as rogue waves on dn, cn, nd and sd periodicity are obtained, and the characteristics and dynamic behaviors of these solutions are explained.</p>

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Newly shaped solitons and rogue waves on several periodic background in the reduced spin Hirota–Maxwell–Bloch system

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Xiaoyi Song,
  • Zhaqilao

摘要

Newly shaped solitons and rogue waves on several periodic background in the reduced spin Hirota–Maxwell–Bloch (rsHMB) system are presented. First, various seed solutions of the rsHMB system are established, including constant solutions and four types of Jacobian elliptic function solutions. Then, by means of the nonlinearization of Lax pairs and the Darboux transformation (DT) method, the general expressions of \(q(x, t)\) and \(\eta (x, t)\) are derived by corresponding several seed solutions including constant solutions, dn, cn, nd and sd solutions, respectively. N-shaped solitons, M-shaped solitons, W-shaped solitons, multi-peaked solitons as well as rogue waves on dn, cn, nd and sd periodicity are obtained, and the characteristics and dynamic behaviors of these solutions are explained.