Large-space and long-time asymptotic behaviors of N_∞-soliton solutions (soliton gas) for the focusing Hirota equation

2024/01/17 by Weifang Weng, Zhenya Yan, Weng, Weifang +1
Mathematics · Physics and Astronomy · #35C20 #35Q15 #35Q51 #37K15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.2401.08924

openalex publication_date 2024/01/17 · openalex created_date 2024/01/19 · openalex updated_date 2026/07/28

Abstract

The Hirota equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation, and can describe the ultra-short optical pulse propagation in the form iq_t+α(q_xx+ 2|q|²q)+iβ(q_xxx+ 6|q|²q_x)=0, (x,t)∈ℝ² (α, β∈ℝ). In this paper, we analytically explore the asymptotic behaviors of a soliton gas for the Hirota equation including the complex modified KdV equation, in which the soliton gas is regarded as the limit N→ ∞ of N-soliton solutions, and characterized using the Riemann-Hilbert problem with discrete spectra restricted in the intervals (ia, ib)∪ (-ib, -ia) (04βb², ξ_c

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