Asymptotic analysis of N-elliptic localized solutions for the Fokas--Lenells equation

Abstract: This paper investigates the N-elliptic localized solutions of the Foka-Lenells equation. Based on the corresponding Lax pair, the Weierstrass elliptic functions are adopted to construct the elliptic function solutions and the fundamental solution matrix of the equation. The N-elliptic localized solutions are further derived via the N-fold Darboux-Backlund transformation. By virtue of the Cauchy determinant expressed with sigma functions, the asymptotic behaviors of the obtained solutions are systematically analyzed along and between their propagation directions, and the symmetry properties of these solutions are established.