Hamiltonian Perturbation Terms Research Articles

Stochastic Perturbation of Optical Solitons for the Concatenation Model with Power-Law of Self-Phase Modulation Having Multiplicative White Noise

Addressing the concatenation model, this paper explores the incorporation of power-law self-phase modulation and spatio-temporal dispersion, in addition to the chromatic dispersion. The inclusion of the white noise effect, along with deterministic Hamiltonian perturbation terms of arbitrary intensity, is also examined. Two integration approaches are applied to recover the soliton solutions, leading to the observation that the white noise effect remains confined to the phase component of these solutions.

Numerical Simulation of Cubic-quartic Optical Soliton Perturbation by the Laplace–Adomian Decomposition

The current paper is on the numerical analysis of bright and dark cubic-quartic solitons that emerges from the Fokas–Lenells equation with Hamiltonian perturbation terms. The Kerr law of nonlinearity is the source of self-phase modulation. The adopted numerical scheme is the Laplace–Adomian decomposition.

Optical wave solutions of the nonlinear Schrödinger equation with an anti-cubic nonlinear in presence of Hamiltonian perturbation terms

In this paper, we study the nonlinear Schrödinger equation with an anti-cubic nonlinear with Hamiltonian perturbation terms by using the complete discrimination system for polynomial. The main result is a complete classification of traveling wave patterns in parameters space from which we can recognize the form of optical wave only based on the physical parameters condition.

BIFURCATIONS AND OBTAINED EXACT SOLUTIONS OF THE OPTICAL SOLITON MODEL IN METAMATERIALS DOMINATED BY ANTI-CUBIC NONLINEARITY

In this paper, we study the optical model in metamaterials with nonlinear influence of non-Kerr law and a few Hamiltonian perturbation terms. The nonlinearity of metamaterials is dominated by anti-cubic type. We apply the approach of dynamical system to find the travelling wave solutions of the optical model. Under different parameter conditions, bifurcations of phase portraits and exact periodic solutions, homoclinic and heteroclinic solutions, peakon, periodic peakons as well as compacton solutions for this planar dynamical system are given. By using the first integral, exact solutions of can be calculated under different parameter conditions. 83 exact explicit parametric representations are derived.

Cubic–Quartic Optical Soliton Perturbation for Fokas–Lenells Equation with Power Law by Semi-Inverse Variation

The current work addresses cubic–quartic solitons to compensate for the low count of the chromatic dispersion that is one of the major hindrances of soliton transmission through optical fibers. Thus, the present paper handles the cubic–quartic version of the perturbed Fokas–Lenells equation that governs soliton communications across trans-oceanic and trans-continental distances. The model is also considered with the power-law form of nonlinear refractive index that is a sequel to the previously reported result. This is a tremendous advancement to the previously known result that was only with the Kerr-law form of nonlinear refractive index. The present paper mainly contributes by generalizing the Kerr law of nonlinearity to the power law of nonlinearity. The prior results therefore fall back as a special case to the results of this paper. The semi-inverse variational principle yields a bright 1-soliton solution that is imperative for the telecommunication engineers to carry out experimental investigation before the rubber meets the road. Hamiltonian perturbation terms are included that come with maximum intensity. The soliton amplitude–width relation is retrievable from a polynomial equation with arbitrary degree. The parameter constraints are also identified for the soliton to exist.

Cubic–quartic optical solitons of perturbed Biswas–Milovic equation having Kudryashov’s nonlinear form and two generalized non-local laws

The present study reveals cubic–quartic optical solitons with the perturbed Biswas–Milovic equation having Kudryashov’s nonlinear form and two generalized non-local laws for the first time. The Hamiltonian perturbation terms are presented via the maximum intensity parameter. Singular, bright-singular and dark solitons are retrieved using two mathematical schemes that are the modified Kudryashov’s procedure and the extended auxiliary equation algorithm. These solitons are extracted via certain restrictions.

Cubic-quartic optical soliton perturbation with Fokas–Lenells equation by semi-inverse variation

This paper recovers cubic-quartic bright optical solitons with perturbed Fokas–Lenells equation. The Hamiltonian perturbation terms appear with maximal permissible intensity. The semi-inverse variational principle is employed to retrieve such solitons.

New optical solitons perturbation in the birefringent fibers for the CGL equation with Kerr law nonlinearity using two integral schemes methods

The researchers in this article are recovering optical soliton solutions (OSS) to the nonlinear complex Ginzburg-Landau (CGL) equation with Hamiltonian perturbation terms in birefringent fibers having Kerr law nonlinearity. Integration schemes are the addendum to extended Kudryashov's (AEK's) method and the addendum to Kudryashov's (AK's) method have made this retrieval possible. Straddled soliton, combo bright-singular soliton (CBSS), bright soliton (BS), dark soliton (DS) and singular soliton (SS) solutions as well as combination between the CBSS solution and combo dark-singular soliton (CDS) solutions, combination between DS solutions and (CDSS) solutions and combination between (SS) solutions and (CDSS) solutions are recovered and enumerated for this model. These two methods are efficient and powerful in solving a wide classes of nonlinear partial differential equations.

Pure-cubic optical soliton perturbation with full nonlinearity by unified Riccati equation expansion

This paper recovers pure-cubic soliton solutions when chromatic dispersion, being negligibly small, is discarded and replenished with third-order dispersion. The governing model is considered with a few Hamiltonian perturbation terms that will sustain the balance between dispersion and self-trapping effect stemming from the nonlinear refractive index. The model is studied with ten forms of nonlinearity. The unified Riccati equation expansion method is the integration algorithm utilized here. This yields dark and singular optical solitons that are all presented along with their respective parameter restrictions.

Pure-cubic optical soliton perturbation with full nonlinearity

This paper studies pure-cubic optical solitons when chromatic dispersion is completely discarded. The third-order dispersion effects are consequently included along with a few Hamiltonian perturbation terms. The governing model is treated with Kerr and power laws of nonlinear refractive index.

Persistent currents by reservoir engineering

We demonstrate that persistent currents can be induced in a quantum system in contact with a structured reservoir, without the need of any applied gauge field. The working principle of the mechanism leading to their presence is based on the extension to the many-body scenario of non-reciprocal Lindblad dynamics, recently put forward by Metelmann and Clerk in Phys. Rev. X 5, 021025 (2015): Non-reciprocity can be generated by suitably balancing coherent interactions with their corresponding dissipative version, induced by the coupling to a common structured environment, such to make total interactions directional. Specifically, we consider an interacting spin/boson model in a ring-shaped one-dimensional lattice coupled to an external bath. By employing a combination of cluster mean-field, exact diagonalization and matrix-product-operator techniques, we show that solely dissipative effects suffice to engineer steady states with a persistent current that survives in the limit of large systems. We also verify the robustness of such current in the presence of additional dissipative or Hamiltonian perturbation terms.

On solving the nonlinear Schrödinger equation with an anti-cubic nonlinearity in presence of Hamiltonian perturbation terms

The soliton ansatz method, the tanh-coth method, the modified simple equation method, the new extended auxiliary equation method, the new mapping method, the rational (G′/G)-expansion method and the generalized Kudryashov method are applied in this paper. Solitons and other solutions for nonlinear Schrodinger equation with an anti-cubic nonlinearity in presence of Hamiltonian perturbation terms have been found. The used methods present a wider applicability for handling the nonlinear partial differential equations. A comparison of our new results with the well-known results is made.

Analysis of optical solitons in nonlinear negative-indexed materials with anti-cubic nonlinearity

This paper adopts the extended trial equation method to handle optical nonlinear negative-index materials that come with anti-cubic nonlinearity. In presence of Hamiltonian perturbation terms, soliton solutions are obtained. These are bright and singular solitons only. However, some additional wave solutions are also emerged.

Resonant optical soliton perturbation with anti-cubic nonlinearity by extended trial function method

This paper studies the resonant optical solitons that comes with anti-cubic nonlinearity in presence of Hamiltonian perturbation terms. The extended trial function method is employed to retrieve cnoidal waves, bright and singular soliton solutions as well as periodic singular solutions to the model.

Chirped optical solitons in nano optical fibers with dual-power law nonlinearity

We investigate the dynamics of ultrashort pulses in nano optical fibers that is governed by improved nonlinear Schrödinger equation with dual-power law nonlinearity with Hamiltonian perturbation terms. A set of entirely new soliton solutions with nonlinear chirp is derived for the first time. The chirped solutions comprise of bright, dark and singular solitons, illustrating the potentially rich set of localized structures with nontrivial phase for the improved model. It was shown that the nonlinear chirp associated with each of these optical solitons is dependent on the pulse intensity. The restrictions on physical parameters for the existence of chirped soliton pulses are also listed.

Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives

This paper studies optical solitons with fractional temporal evolution in presence of Hamiltonian perturbation terms. The three types of nonlinearity are Kerr law, parabolic law and dual-power law. The first integral method with conformable fractional derivative is applied to retrieve soliton solutions to the model. Several constraint conditions guarantee the existence of such solitons.

Optical Solitons with Power Law Nonlinearity and Hamiltonian Perturbations: An Exact Solution

This paper studies the optical solitons with power law nonlinearity in presence of Hamiltonian perturbation terms. The perturbation terms that are taken into account are inter-modal dispersion, third order dispersion, self-steepening term and nonlinear dispersion. An exact 1-soliton solution is obtained by the solitary wave ansatz. Both bright and dark optical soliton solutions are obtained. The domain restrictions have also been identified in the process.

Canonical harmonic tracking of charged particles in circular accelerators

Harmonic tracking is a method used to study non-linear particle dynamics in a circular accelerator. The tracking algorithm is based on numerical solution of the Hamilton equations of motion. An essential feature of the method is the approximation of Hamiltonian perturbation terms by a finite number of azimuthal harmonics, which provides an effective tool for optimization of non-linear particle motion. The equations of motion are solved canonically, with the first-order prediction made using the explicit Lie transformation. The major features of harmonic tracking are presented and examples of its application are discussed.