2025/01/07 by Weifang Weng, Zhenya Yan, Weng, Weifang +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2501.03485
openalex publication_date 2025/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explore the N∞-soliton asymptotics for the modified Camassa-Holm (mCH) equation with linear dispersion and boundaries vanishing at infinity: mt+(m(u2-ux2)2)x+κux=0, m=u-uxx with limx→ ± ∞ u(x,t)=0. We mainly analyze the aggregation state of N-soliton solutions of the mCH equation expressed by the solution of the modified Riemann-Hilbert problem in the new (y,t)-space when the discrete spectra are located in different regions. Starting from the modified RH problem, we find that i) when the region is a quadrature domain with ℓ=n=1, the corresponding N∞-soliton is the one-soliton solution which the discrete spectral point is the center of the region; ii) when the region is a quadrature domain with ℓ=n, the corresponding N∞-soliton is an n-soliton solution; iii) when the discrete spectra lie in the line region, we provide its corresponding Riemann-Hilbert problem,; and iv) when the discrete spectra lie in an elliptic region, it is equivalent to the case of the line region.