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math.AP2025
Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities
Yuan Li, Qiaoyuan Cheng, Engui Fan
We establish the global existence of solutions to the Fokas-Lenells equation for any initial data in a weighted Sobolev space .This resul…
math-ph2025
Soliton resolution, asymptotic stability and Painlevé transcendents in the combined Wadati-Konno-Ichikawa and short-pulse equation
Yidan Zhang, Engui Fan
In this paper, we develop a Riemann-Hilbert (RH) approach to the Cauchy problem for the combined Wadati-Konno-Ichikawa and short-pulse (WKI-SP) equation. The solution of the Cauchy…
math-ph2025
Riemann-Hilbert approach to the Algebro-Geometric solution of the modified Camassa-Holm equation with linear dispersion term
Engui Fan, Gaozhan Li, Yiling Yang
This paper aims at providing an exact algebro-geometric solution of the modified Camassa-Holm (mCH) equation derived from hyperelliptic curves in genus. To achieve this…