Michelle Savescu

Singular solitons in optical metamaterials by ansatz method and simplest equation approach

This paper derives singular 1-soliton solution for optical metamaterials. There are two integration approaches that obtains the solution. These are the ansatz approach and the simplest equation approach. The second method also leads to an additional set of solutions that emerge as a by-product. These are topological soliton, rational solution and singular periodic solution. The constraint conditions for the existence of these solutions are also exhibited. The numerical simulation of a topological 1-soliton solution is also exhibited.

Optical solitons in nonlinear directional couplers with spatio-temporal dispersion

This paper addresses solitons in nonlinear directional couplers in non-Kerr law media, with spatio-temporal dispersion. Both twin-core couplers as well as multiple-core couplers are studied. The nonlinearities studied are Kerr law, power law, parabolic law, dual-power law and log law. Bright, dark and singular soliton solutions of the governing equation are studied.

Dispersive optical solitons with Schrodinger-Hirota equation

The dynamics of dispersive optical solitons, modeled by Schrodinger–Hirota equation, are studied in this paper. Bright, dark and singular optical soliton solutions to this model are obtained in presence of perturbation terms that are considered with full nonlinearity. Soliton perturbation theory is also applied to retrieve adiabatic parameter dynamics of bright solitons. Optical soliton cooling is also studied. Finally, exact bright, dark and singular solitons are addressed for birefringent fibers with perturbation terms included.

Optical solitons in DWDM system with spatio-temporal dispersion

This paper obtains bright, dark and singular soliton solutions to dense wavelength division multiplexed (DWDM) system, with spatio-temporal dispersion. There are two types of nonlinear media that are considered and they are Kerr law and parabolic law. Four integration algorithms are applied to retrieve these solitons. They are G′/G-expansion scheme, extended tanh function approach, Kudryashovs algorithm and finally the ansatz method. The results follow with respective constraints that guarantees the existence of solitons.

OPTICAL SOLITON PERTURBATION IN NANOFIBERS WITH IMPROVED NONLINEAR SCHRÖDINGER'S EQUATION BY SEMI-INVERSE VARIATIONAL PRINCIPLE

This paper studies the perturbation of the improved version of the nonlinear Schrodingers equation that governs the propagation of solitons through nonlinear optical fibers. The semi-inverse variational principle is employed in order to obtain an analytical soliton solution in presence of the perturbation terms. There are three types of nonlinearity that will be studied. They are Kerr law, power law and the log law. The constraint conditions will naturally fall out in order for the soliton solutions to exist. The numerical simulations supplement the analytical results for each of the three laws of nonlinearity.

Optical Solitons in Magneto-optic Waveguides with Spatio-temporal Dispersion

Abstract This paper obtains the exact solution for solitons propagating through magneto-optic waveguides. There are three forms of nonlinear media that are considered. They are Kerr law, power law and log-law nonlinearity. The ansatz approach retrieves bright, dark as well as singular soliton solutions. There are several constraint conditions that needs to be in place for the solitons and Gaussons to exist.

Conservation laws for optical solitons with spatio-temporal dispersion

The conservation laws for optical solitons with spatio-temporal dispersion are obtained in this paper. There are three conserved quantities that are reported in this paper. They are the power, linear momentum, and the Hamiltonian. The conserved quantities, from their respective densities, are obtained from 1-soliton solution that was reported earlier. Five types of nonlinear media are taken into account.

SOLITONS AND CONSERVATION LAWS IN NEUROSCIENCES

This paper obtains the 1-soliton solution by the ansatz method for the proposed model that governs the propagation of solitons through the neurons. This model is an improved one that describes the solitons in neurosciences more accurately. The ansatz method is applied to obtain the 1-soliton solution to the model. The Lie symmetry analysis is subsequently applied to obtain the conservation laws for the model.

Solitary wave propagation in tunable liquid crystal-filled dual-core photonic crystal fibers

ABSTRACT In this paper, we introduce the mathematical model and the necessary constraint conditions of solitary wave propagation through dual core photonic crystal fibres (PCF) filled with liquid crystal. Using the Ansatz method, we derived analytically the necessary formulas to support soliton wave propagation in the new proposed type of coupled bi-refringent fibres. We evaluated dispersion and coupling coefficients by solving wave equations using the vector finite element method. These values can be tuned either by applying external perturbations such as heat or electric field or even altering the geometry of the PCF. Based on the constraint conditions derived from analytic formulas and numerical simulation, we determined the wavelength range for which the soliton waves will be supported without any distortion. The wavelength range can be adjusted by tuning the PCF.