Bright solitons on a cnoidal wave background for the inhomogeneous nonlinear Schrödinger equation

Abstract

In this paper, we investigate the bright solitons on a cnoidal wave background train of the inhomogeneous nonlinear Schrödinger equation, which may be applicable to many physically realizable systems such as Bose–Einstein condensation media and plasma, etc. We use well-known methods to reduce the inhomogeneous nonlinear Schrödinger equation to a standard nonlinear Schrödinger equation by using the combination of Husimi's and Lens-type transformations. We study the superposed configuration of soliton with a cnoidal wave solution of the underlying equation. Finally, we discuss the dynamics of soliton on a cnoidal wave background in Bose–Einstein condensation trapped in linear density and harmonic density profiles separately.

Loss of stability of a solitary wave through exciting a cnoidal wave on a Fermi-Pasta-Ulam ring

“…In the framework of the one-dimensional NLS equation, the interaction of solitons (envelope solitons) with radiation (a nonsoliton part) [42], continuous waves having constant amplitude [43], cnoidal waves [44], and continuous waves of arbitrary shape [45] has been studied both analytically and numerically. The bright solitons on a cnodial wave background train of the inhomogeneous NLS equation have also been investigated [46]. The theoretical analysis of the interaction between the solitons and the cnoidal waves in the NLS equation (integrable) is based on the construction of the exactly superposed solutions of these two waves.…”

Spatial bright and dark similaritons on cnoidal wave backgrounds in 2D waveguides with different distributed transverse diffractions

“…Many theoretical works have been done to discuss the characteristics of solitons lying on a cnw [9][10][11][12]. Shin [9] analyzed the scattering of a soliton from a cnw train in a fiber theoretically as well as numerically.…”

“…Then he [10] investigated multisoliton complexes moving on a cnw background, and discussed the peculiar phenomenon of multisoliton complexes shifting the crests of cnoidal waves. Murali et al [11] investigated the bright solitons on a cnw background train. Solitons crossing the cnw and travelling in parallel with the cnw were studied [11].…”

“…Murali et al [11] investigated the bright solitons on a cnw background train. Solitons crossing the cnw and travelling in parallel with the cnw were studied [11]. Moreover, Shin [12] found a solution of the dark soliton lying on a cnw background in a defocusing medium.…”

Soliton dynamics in phase-modulated lattices

“…For the special case of solitons propagating on a one-dimensional geometry and on a cnoidal-type background lattice, theoretical analyses exist based on the nonlinear Schrödinger (NLS) equation [10,11] or on the coupled NLS equations [3,4,8,9]. Some of these analyses are based on the Darboux transformation and they use the so-called Sym's solution [12].…”