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We investigate exact soliton solutions with nonlinear chirp for the coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity, self-steepening, self-frequency shift and four-wave mixing. The model governs the femtosecond pulse propagation in birefringent fibers. We introduce a new ansatz to obtain the nonlinear chirp associated with the propagating soliton pulses. New chirped soliton pair solutions with non-trivial chirping are found for the coupled nonlinear equations, illustrating the potentially rich set of solitonic pulse solutions of the model with higher-order effects. The solutions comprise two types of bright-W-shaped and bright-bright soliton pairs as well as kink and anti-kink pulses. Interestingly, the bright wave in the bright-W shaped soliton pairs possesses a platform underneath it, originating from the self-steepening and self-frequency shift effects. The corresponding chirp associated with each of these optical soliton pairs is also determined. It is shown that the nonlinear chirp is related to the pair intensity and determined by self-frequency shift and pause self-steepening. Parametric conditions for the existence and uniqueness of chirped solutions are given. [ABSTRACT FROM AUTHOR]

A theoretical investigation of the propagation of a relativistic electron (or positron) particle beam in an overdense magnetoactive plasma is carried out within a fluid plasma model, taking into account the individual quantum properties of beam particles. It is demonstrated that the collective character of the particle beam manifests mostly through the self-consistent macroscopic plasma wakefield created by the charge and the current densities of the beam. The transverse dynamics of the beam–plasma system is governed by the Schrödinger equation for a single-particle wavefunction derived under the Hartree mean field approximation, coupled with a Poisson-like equation for the wake potential. These two coupled equations are subsequently reduced to a nonlinear, non-local Schrödinger equation and solved in a strongly non-local regime. An approximate Glauber solution is found analytically in the form of a Hermite–Gauss ring soliton. Such non-stationary (‘breathing’ and ‘wiggling’) coherent structure may be parametrically unstable and the corresponding growth rates are estimated analytically. [ABSTRACT FROM PUBLISHER]

generic nonlocal nonlinear optical system with a diffusive type of nonlinearity is investigated analytically, using the homogeneous balance principle and the F-expansion technique. Exact traveling wave and soliton solutions are discovered. Numerical simulation of their propagation and interaction properties is carried out. Our results demonstrate that the nonlocal solitary waves can be manipulated and controlled by changing the nonlocality parameter. [ABSTRACT FROM AUTHOR]

Bright and dark matter wave solitons are constructed analytically in a three-dimensional (3D) highly anisotropic Bose-Einstein condensate (BEC) with a time-dependent parabolic potential, and numerical simulations are performed to confirm the existence and dynamics of such analytical solutions. Different classes of bright and dark solitons are discovered among the solutions of the generalized anisotropic (3+1)D Gross-Pitaevskii equation. Our results demonstrate that the bright and dark solitary waves can be manipulated and controlled by changing the scattering length, which can be used to compress the second-order bright and dark solitons of BECs into desired peak density. [ABSTRACT FROM AUTHOR]