2024/07/07 by Xiaoen Zhang, Liming Ling, Zhang, Xiaoen +1
Mathematics · Physics and Astronomy · #35Q15 #35Q51 #35Q55 #37K10 #37K15 #37K40 #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2407.05384
openalex publication_date 2024/07/07 · openalex created_date 2024/07/10 · openalex updated_date 2026/07/28
In this paper, we consider a soliton gas of the focusing modified Korteweg-de Vries generated from the N-soliton solutions under the nonzero background. The spectral soliton density is chosen on the pure imaginary axis, excluding the branch cut Σc=[-i, i]. In the limit N→∞, we establish the Riemann-Hilbert problem of the soliton gas. Using the Deift-Zhou nonlinear steepest-descent method, this soliton gas under the nonzero background will decay to a constant background as x→+∞, while its asymptotics as x→-∞ can be expressed with a Riemann-Theta function, attached to a Riemann surface with genus-two. We also analyze the large t asymptotics over the entire spatial domain, which is divided into three distinct asymptotic regions depending on the ratio ξ=(x)/(t). Using the similar method, we provide the leading-order asymptotic behaviors for these three regions and exhibit the dynamics of large t asymptotics.