Spectral analysis and soliton structures for the Hermitian symmetric space Fokas–Lenells equation

Based on the spectral analysis and inverse scattering method, we construct a Riemann–Hilbert problem related to the solution of the Hermitian symmetric space Fokas–Lenells equation. Because this equation is a negative flow associated with the higher-order matrix spectral problem, it is very difficult to study it. Therefore, we have to start spectral analysis from the t-part of the Lax pair other than the x-part to obtain enough analytic spectral functions formulating the desired Riemann–Hilbert problem. The corresponding Riemann–Hilbert problem is derived by the t-part of the Lax pair with the x-part playing only an auxiliary role. The zero structures of the Riemann–Hilbert problem are revealed, from which N-soliton solutions of the Hermitian symmetric space Fokas–Lenells equation are obtained by solving the nonregular Riemann–Hilbert problem under the reflectionless case. In addition, the interaction dynamics of the multi-soliton solutions are analyzed by choosing appropriate parameters.