In this paper, we study the N-soliton solutions for Hirota-Maxwell-Bloch system (H-MB system) via Riemann-Hilbert approach. By a Lax pair of this system, the inverse scattering method is employed to construct a Riemann-Hilbert problem (RHP) for the H-MB system under a non-zero background, which is imposed only on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\eta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation> component (with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$u,p \rightarrow 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>u</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> as <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$x \rightarrow \pm \infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo stretchy="false">→</mo> <mo>±</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>). From this RHP, the long-time asymptotics of the soliton is derived, and the N-soliton solutions are obtained, with explicit expressions given for the cases <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$N=1,2,3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. Furthermore, the dynamical properties of the case where <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$N=1,2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> are investigated, and the corresponding three-dimensional plots are presented. Compared with the conclusions reported under specific parameter choices, the results obtained in this paper are valid for general parameters <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>. This is of great significance for the study of nonlinear pulse propagation in optical fibers.

Inverse scattering transform and soliton solutions for the coupled Hirota-Maxwell-Bloch system with nonzero background

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发表日期：

2026年6月14日

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Shuai Liu,
Yaqing Liu

摘要

In this paper, we study the N-soliton solutions for Hirota-Maxwell-Bloch system (H-MB system) via Riemann-Hilbert approach. By a Lax pair of this system, the inverse scattering method is employed to construct a Riemann-Hilbert problem (RHP) for the H-MB system under a non-zero background, which is imposed only on the $\eta $ $η$ component (with $u,p \rightarrow 0$ $u, p \to 0$ as $x \rightarrow \pm \infty $ $x \to \pm \infty$ ). From this RHP, the long-time asymptotics of the soliton is derived, and the N-soliton solutions are obtained, with explicit expressions given for the cases $N=1,2,3$ $N = 1, 2, 3$ . Furthermore, the dynamical properties of the case where $N=1,2$ $N = 1, 2$ are investigated, and the corresponding three-dimensional plots are presented. Compared with the conclusions reported under specific parameter choices, the results obtained in this paper are valid for general parameters $\alpha $ $α$ and $\beta $ $β$ . This is of great significance for the study of nonlinear pulse propagation in optical fibers.