Kummer solitons in strongly nonlocal nonlinear media

We solve the three-dimensional (3D) time-dependent strongly nonlocal nonlinear Schrödinger equation (NNSE) in spherical coordinates, with the help of Kummer's functions. We obtain analytical solitary solutions, which we term the Kummer solitons. We compare analytical solutions with the numerical solutions of NNSE. We discuss higher-order Kummer spatial solitons, which can exist in various forms, such as the 3D vortex solitons and the multipole solitons.     

Three-dimensional spatiotemporal solitary waves in strongly nonlocal media

We construct a class of three-dimensional strongly nonlocal spatiotemporal solitary waves of the nonlocal nonlinear Schrödinger equation, by using superpositions of single accessible solitons as initial conditions. Evolution of such solitary waves, termed the accessible light bullets, is studied numerically by choosing specific values of topological charges and other solitonic parameters. Our numerical results reveal that in strongly nonlocal nonlinear media with a Gaussian response function, different classes of accessible spatiotemporal solitons can be generated and controlled by tailoring different soliton parameters.     

Optical soliton perturbation with full nonlinearity by extended trial function method

The extended trial function scheme is applied to retrieve soliton solutions to the perturbed nonlinear Schrödinger’s equation with ten forms of fiber nonlinearity. Bright, dark and singular soliton solutions are retrieved that appear with their respective existence criteria. Some additional forms of nonlinear waves naturally emerge as a byproduct of the integration scheme.     

Transport properties in the photonic super‐honeycomb lattice — a hybrid fermionic and bosonic system

We report on the transport properties of the super‐honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight‐binding approximation. The super‐honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. It also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat‐band mode of the super‐honeycomb lattice will be excited and the input beams will exhibit strong localization during propagation. On the other hand, if the modes of Dirac cones of the super‐honeycomb lattice are excited, one will observe conical diffraction. Furthermore, if the input beam is properly chosen to excite a sublattice of the super‐honeycomb lattice and the modes of Dirac cones with different pseudospins, e.g., by the three‐beam interference pattern, the pseudospin‐mediated vortices will be observed.

     

Systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds

In almost all real-world application such as electric vehicles, system outputs are corrupted by various types of noises. Although the sliding mode controller is a popular controller in the electrical vehicle applications, it is vulnerable to the noisy signals, and even intensify its unwilling effects. In this paper, to eliminate process noise and stabilize the vehicle in noisy conditions, a minimum variance controller is utilized. It is shown that this controller is able to decrease the system output variance, optimally. Besides, it can track yaw rate and velocity reference inputs. Also stability condition is reached. Furthermore, decreasing control signal variance along with output variance is studied in this paper. Finally, the proposed approach is compared with sliding mode controller in noisy condition on four wheel drive electric vehicle which is simulated in MATLAB and CARSIM environments.     

Superpositions of Laguerre-Gaussian Beams in Strongly Nonlocal Left-handed Materials

We present beam solutions of the strongly nonlocal nonlinear Schrödinger equation in left-handed materials (LHMs). Different Laguerre-Gaussian (LG) necklace beams, such as symmetric and asymmetric single layer and multilayernecklace beams are created by the superposition of two single beams with different topological charges. Such superpositions are then propagated through LHMs, displaying linear diffraction. It is found that the superposition of two LG_nm beams with opposite topological charges does not show rotational behavior and that there exists rotation for other topological charge combinations. Our theory predicts that the accessible solitons cannot exist in LHMs.     

Bright soliton interactions in a $$\mathbf (2 +\mathbf 1) $$ ( 2 + 1 ) -dimensional fourth-order variable-coefficient nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin chain

Nonlinear Dynamics - Interactions of bright solitons in the Heisenberg ferromagnetic spin chain, governed by a $$(2+1)$$ -dimensional nonlinear Schrödinger equation with variable coefficients,...     

Solitons for perturbed Gerdjikov–Ivanov equation in optical fibers and PCF by extended Kudryashov’s method

This paper reveals bright, dark and singular soliton solutions to the perturbed Gerdjikov–Ivanov equation by the aid of extended Kudryashov’s method. The nonlinear terms appear with full nonlinearity in order to give a generalized flavor to the model. As a byproduct of this scheme, plane waves and singular periodic solutions fall out and these solutions are listed as well.     

Reactant adsorption in cyclic staircase voltammetry on spherical microelectrodes. Reversible redox reactions

On spherical microelectrodes, cyclic staircase voltammograms of reversible redox reactions complicated by the reactant adsorption depend on lateral interactions in the monolayer. Attraction forces increase the separation between the main wave and the post-peak, while the repulsion prevents the resolution of responses of the surface and volume reactions. The theoretical relationships between the dimensionless responses and the dimensionless adsorption constant, the relative surface adsorption capacity, the Frumkin coefficient and the electrode sphericity are given.