Stability of kink, anti kink and dark soliton solution of nonlocal Kundu–Eckhaus equation

Abstract

We study the modulational instability and soliton solution for nonlocal Kundu–Eckhaus (KE) equation which is distinctly different from KE equation. KE equation can describe the dynamical behavior of optical pulse envelopes in birefringent fiber. Although, the present equation has novel space, which induce new physical effects and inspire novel physical applications. Therefore, through the Jacobi elliptic function method, the elliptic function solution is derived for the nonlocal KE. Deng et al. (2022) found the N-soliton solution for nonlocal KE equation by the use of Hirota bilinear method. Though, the present problem of the solution is new which is Jacobi elliptic function solution. It is found that the solution exhibits a variety of forms of soliton as dark, kink and antikink soliton due to distinct choices of values of focusing and defocusing parameters. Importantly, with the use of the Jacobi elliptic solution, the role of focusing and defocusing parameters of cubic, quintic nonlinearity and self frequency shift on optical soliton in birefringent fiber for nonlocal KE equation is discussed. The linear stability analysis is used to construct the gain of nonlocal Kundu–Eckhaus equation and using it to analysis the stability/instability of various forms of soliton.