Soliton structures in the (1+1)-dimensional Ginzburg–Landau equation with a parity-time-symmetric potential in ultrafast optics

Li Wenyi^{1, 2}, Ma Guoli^{1, 2}, Yu Weitian¹, Zhang Yujia¹, Liu Mengli^{1, 2}, Yang Chunyu¹, Liu Wenjun^{1, 2, †}

(color online) Different soliton structures of A(z,x) with the appropriate parameters as: ε = 1, k₁ = 1, k₂ = 0.75, c₁ = 2, c₂ = 1, and θ_i = 1 (i = 1,2). (a) Periodic wave structure w 1 ( x ) = x + cos ( x ) − 1 and w 2 ( x ) = 0.1 sin ( x ) . (b) Soliton-like structure w 1 ( x ) = x + 0.8 e − x 2 and w 2 ( x ) = 0.1 sin ( x ) . (c) Solition-like structure w 1 ( x ) = x − 0.5 e − x 2 and w 2 ( x ) = 0.1 sin ( x ) . (d) Single soliton structure w 1 ( x ) = x and w 2 ( x ) = 0.1 sin ( x ) .