Discrete soliton solutions for a generalized discrete nonlinear Schrödinger equation with variable coefficients via discrete N -fold Darboux transformation

Localized wave solutions to a variable-coefficient coupled Hirota equation in inhomogeneous optical fiber

“…The variable coefficient equations are applied to describe localized waves, which consist of solitons [19,20], breathers [21], and rogue waves [22,23]. Several methods are used to investigate localized waves, including Darboux transformation (DT) [24][25][26], Bäcklund transformation [27], and bilinear methods [28,29]. The study of localized waves in nonlinear optical fiber using the variable coefficient equations have provided the theoretical basis for modern communication [30,31].…”

Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation*

“…[20] In recent years, different soliton solutions of GCNLS equation have been extensively studied. [21][22][23][24][25][26][27][28][29][30][31][32] In 2010, two-soliton solution of GCNLS equation and the collision dynamics between solitons were studied in Ref. [16], and a new soliton phenomenon (soliton reflection) was found.…”

“…Later, the dark-dark soliton, general breather solution (GB), Akhmediev breather solution (AB), Ma soliton solution (MS), and rouge wave solution (RW) of GCNLS equation were obtained by use of Hirota bilinear method. [23][24][25][26][27][28][29][30][31] The N-soliton solutions of the GCNLS equation with four-wave mixing effect were presented and the collision properties of one-soliton, two-soliton, and three-soliton solutions have also been studied in detail in Ref. [17].…”