Application of the Riemann–Hilbert Approach and \(N\)-soliton Solutions for the Generalized Fokas–Lenells Equation

This paper investigates the generalized Fokas–Lenells equation by the Riemann–Hilbert approach. A gauge transformation is introduced to symmetrize the originally asymmetric spectral problem. A novel Riemann–Hilbert method is developed for the generalized Fokas–Lenells equation, performing spectral analysis on the temporal component of the Lax pair rather than the spatial part. \(N\)-soliton solutions are rigorously derived by solving the Riemann–Hilbert problem with this complex spectral symmetry. Additionally, the dynamics of the one and two solitons of the generalized Fokas–Lenells equation are discussed. Abstract Published by the Jagiellonian University 2025 authors