Wide vector solitons in systems with time- and space-modulated nonlinearities

Abstract

In this work we apply point canonical transformations to solve some classes of two coupled nonautonomous nonlinear Schrödinger equations with specific cubic and quintic-time-and space-dependent-nonlinearities. The method applied here allows us to find a class of wide localized (in space) vector soliton solutions of nonautonomous nonlinear Schrödinger equations. The vector solitons found here can be applied to theoretical studies of Bose-condensed atoms in two different internal states and of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities.

Vector solitons in an extended coupled Schrödinger equations with modulated nonlinearities

“…It has been shown in [19] that the dynamics of the ultrashort pulse propagation along orthogonal polarization axes in nonlinear optical fibers with Kerr and non-Kerr nonlinearities may be governed by a system of coupled non-autonomous NLSEs with terms of cubic and quintic order in the wave function:…”

“…The functions g jl (x, t), f jl (x, t) and h jl (x, t) describe the strength management of the cubic and quintic (Kerr and non-Kerr) nonlinearities, respectively, m j (t) is the dispersion parameter, and Γ j (t) is the amplification/absorption coefficient (i.e., Γ j > 0 or Γ j < 0, respectively), for more details see [19]. It was shown in [19] by using the method developed in [20] and by imposing specific constraints on the parameters of the equations (1) and (2) that the system described by coupled CQNLSEs Eqs. (1) and (2) can support the propagation of a class of wide localized A C C E P T E D M A N U S C R I P T (in space) vector soliton solutions.…”

“…Vector solitons in the form of periodic-periodic, dark-dark, bright-bright, and dark-bright solitons obtained from a system of two coupled Schrödinger equations (CNLSEs) were studied by Cardoso et al [18]. Arroyo et al [19] went on and extended the model investigated in [18]. They found vector solitons solutions from a system of two coupled non-autonomous cubic-quintic (CQ)NLSEs by considering both two-and three-body interactions and nonKerr-nonlinearity media for the case of BECs and optical fibers, respectively [19].…”

“…They found vector solitons solutions from a system of two coupled non-autonomous cubic-quintic (CQ)NLSEs by considering both two-and three-body interactions and nonKerr-nonlinearity media for the case of BECs and optical fibers, respectively [19]. To search for different vector solitons of the coupled non-autonomous CQNLSEs in [19] it was proposed to use the point canonical transformations [20] and to make an analogy between the autonomous equations and the static equations of motion of a model of two interacting scalar fields in super-symmetric field theory [20]. Then to find topological solutions of the two coupled autonomous CQNLSEs, the orbit equation method [21] was used.…”

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrödinger equation

“…[10], and later in Refs. [11,12], and the point canonical transformations [13], which explains the origin of the ansatz involved in the similarity transformation method.…”