Nonlocal Law Research Articles

Sequel to “Highly dispersive optical solitons with differential group delay for kerr law of self—phase modulation by sardar sub—equation approach”: non—local law of self—phase modulation

AbstractThe paper obtains highly dispersive optical solitons with nonlocal law of self—phase modulation with differential group delay. The Sardar sub equation approach is the integration algorithm that makes this retrieval possible. The parameter constraints that naturally emerge from the scheme are also enlisted. The current work is thus a sequel to the previous paper that is with Kerr law of self—phase modulation structure.

Non-classical theory of electro-thermo-elasticity incorporating local mass displacement and nonlocal heat conduction

A non-classical local gradient theory of nonferromagnetic thermoelastic dielectrics is presented, incorporating both the local mass-displacement process and the heat-flux gradient effect. The process of local mass displacement is related to the changes in material microstructure. The nonlocal heat conduction law is also addressed in the model. Thus, the generalized relationship between the higher-grade heat and entropy fluxes is adopted. The gradient-type constitutive relations and governing equations are derived using the fundamental principles of continuum mechanics, non-equilibrium thermodynamics, and electrodynamics. Due to the contribution of higher-grade flux, the nonlocal law of heat conduction is obtained. The constitutive relations for isotropic materials with the corresponding additional material constants are derived. To illustrate the local gradient theory and to show the electro-thermo-mechanical coupling effect in isotropic materials, a straightforward problem is analytically solved for a layered non-piezoelectric structure under non-uniform temperature distribution. The analytical results reveal that the thermal polarization effect can also be pronounced in isotropic materials. To illustrate the model considering the effect of nonlocal heat conduction, the propagation of spherical thermoelastic harmonic waves in a homogeneous and isotropic elastic medium with non-classical heat conduction law is studied.

Dynamics on novel wave structures of non-linear Schrödinger equation via extended hyperbolic function method

In this study, our focus is on the construction of novel soliton solutions of non-linear Schrödinger equation with parabolic law and non-local law non-linearities via new extended hyperbolic function method. The acquired solutions are original and could be helpful in the field of nonlinear optics, fluid dynamics, and plasma physics. From these outcomes, it is believed that this method is a promising technique to handle a wide variety of such type of equations. For physical understanding and better realization of our constructed solutions, some of the obtained solutions under appropriate parameters are demonstrated by 2D and 3D plots. Analysis discloses that the proposed scheme is consistent and can be applied to more advanced models in engineering and physics.

Highly Dispersive Optical Solitons with Four Forms of Self-Phase Modulation

This paper implements the enhanced Kudryashov approach to retrieve highly dispersive optical solitons and study it with four nonlinear forms. These are the power law, generalized quadratic-cubic law, triple-power law, and the generalized non-local law. This approach reveals bright and singular optical solitons along with the respective parameter constraints.

Optical Solitons in Fiber Bragg Gratings with Dispersive Reflectivity Having Five Nonlinear Forms of Refractive Index

This paper implements the trial equation approach to retrieve cubic–quartic optical solitons in fiber Bragg gratings with the aid of the trial equation methodology. Five forms of nonlinear refractive index structures are considered. They are the Kerr law, the parabolic law, the polynomial law, the quadratic–cubic law, and the parabolic nonlocal law. Dark and singular soliton solutions are recovered along with Jacobi’s elliptic functions with an appropriate modulus of ellipticity.

ANALYSIS OF VISCOPLASTIC CONTACT PROBLEM

In this paper, we analyze a quasistatic problem modeling frictional contact between a viscoplastic body and an obstacle, the so called foundation. The material constitutive relation is assumed to be non-linear. The boundary conditions of contact and friction are modeled respectively by the \textit{Signorini} conditions and the generalized Coulomb's non-local law. We derive a variational formulation for the problem and prove the existence of its unique weak solution. The proof use, essentially, classical arguments of compactness, variational inequalities and Banach’s fixed point theorem.

Structures solitons in birefringent fibers with Kerr and non-local laws of refractive index using improved modified extended tanh-function method

In this article, the improved modified extended tanh-function method is used to construct new structure of highly dispersive optical solitons for nonlinear Schrödinger equation in birefringent fibers with Kerr law and non-local law of refractive index. Bright solitons, dark solitons, bright–dark combo solitons and singular solitons are obtained. Also, periodic solutions, singular periodic solutions, hyperbolic solutions, rational-type solutions and exponential solutions are reported. After giving suitable values to parameters, the novel structures of solutions are depicted. The physical surfaces of some gained solutions in different forms are shown graphically. The results show the superiority of executed method.

Kinky breathers, W-shaped and multi-peak soliton interactions for Kudryashov's quintuple power-law coupled with dual form of non-local refractive index structure

This paper addresses interaction of multi–wave solutions of the model having Kudryashov's quintuple form coupled with dual form of nonlocal law of refractive index. These waves are kinky breathers, W–shaped and multi–peaked solitons. The analytical results are supplemented with numerical simulations of the obtained solutions.OCIS codes060.2310; 060.4510; 060.5530; 190.3270; 190.4370.

Cubic-quartic optical solitons in couplers with optical metamaterials having parabolic non-local law nonlinearity

The main goal of this article is to investigate the optical soliton solutions for the cubic–quartic (CQ) twin-core couplers and multiple-core couplers having optical metamaterials with parabolic non-local law nonlinearity and nonlinear perturbation terms. The couplings with nearest neighbors and with all neighbors are discussed. The unified Riccati equation expansion approach and the addendum to Kudryashov’s approach are applied. Straddled, combo-bright-singular, dark, bright, singular solitons solutions as long as periodic and rational solutions are found.

Optical solitons and other solutions for coupled system of nonlinear Schrödinger’s equation with parabolic nonlocal law of refractive index by using the improved modified extended tanh function method

In this paper, the improved modified extended tanh function method is applied to secure optical soliton solutions in magneto-optic waveguides for coupled system of non-linear Schrödinger equation with parabolic non-local law of refractive index. Bright soliton solutions, dark soliton solutions and singular soliton solutions are obtained. Moreover, for the physical illustration of the obtained solutions, 3D and their corresponding 2D graph are presented.

New private types for the cubic-quartic optical solitons in birefringent fibers in its four forms of nonlinear refractive index

From the point of view of the extended simple equation method, multiple new private distinct types for the cubic-quartic optical soliton birefringent fibers with four forms nonlinear refractive index have been extracted. The suggested model has vital effective effect in all modern telecommunications process. The suggested method which has invited for this purpose examined previously for many other nonlinear problems arising in various branches of science and continuously gives good results. We will implement this method to extracting multiple new private types for the cubic-quartic soliton with its four different forms of the NLSE which are, the cubic-quartic in polarization-preserving fibers with the kerr-low nonlinearity, quadratic-cubic law nonlinearity, parabolic law nonlinearity and non-local law nonlinearity. Actual comparison between our achieved results and that realized previously by other authors has been established.

Cubic-quartic optical solitons in Bragg gratings fibers for NLSE having parabolic non-local law nonlinearity using two integration schemes

The optical solitons in Bragg gratings fibers are studied for NLSE having cubic-quartic dispersive reflectivity with parabolic non-local combo law of refractive index. The extended auxiliary equation method and the addendum to Kudryashov’s method are introduced. The existence criteria for such solitons are indicated.

Cubic–quartic optical solitons with Kudryashov's arbitrary form of nonlinear refractive index

The focus of attention in this paper is to retrieve cubic–quartic solitons in presence of Kudryashov's law including generalized non-local law. The two integration approaches are also due to Kudryashov. A range of soliton solutions have been recovered in the work.

Cubic-quartic optical soliton perturbation in polarization-preserving fibers with complex Ginzburg-Landau equation having five nonlinear refractive index structures

In this research, we present a comprehensive coverage of soliton solutions to perturbed cubic-quartic (CQ) nonlinear complex Ginzburg-Landau (NLCGL) equation with five nonlinear laws to the refractive index. We specialize in studying the nonlinearity in the five different forms: Kerr law, parabolic law, polynomial law, quadratic-cubic law and parabolic non-local law. The integration scheme, namely the addendum to Kudryashov's approach has made this retrieval possible. For five laws nonlinearity, the analytical solutions are clearly constructed the combo-bright-singular, bright, dark and singular optical soliton solutions.

Highly dispersive optical solitons with non-local law of refractive index by Laplace-Adomian decomposition

This paper studies bright highly dispersive optical solitons that are with nonlocal type of nonlinearity. The numerical scheme, adopted in the paper, is Laplace-Adomian method. The analytical results, reported earlier, and the numerical results from the current work, agree with an impressively small error measure.

Cubic–quartic nonlinear Schrödinger equation in birefringent fibers with the presence of perturbation terms

ABSTRACT In this paper, we derive the solitons solutions to the cubic–quartic nonlinear Schrödinger equation (CQ-NLSE) in birefringent fibers with three laws of nonlinearity. These laws are parabolic law, quadratic-cubic law and non-local law. The new extended generalized Kudryashov method and our new method proposed for the first time have been applied. Many solutions have been found. Dark, bright and singular soliton solutions existed under constraint conditions. The comparative analysis of the two proposed methods shows that in the two cases of parabolic and non-local laws, the first method gives the dark and singular solitons in terms of tanh–coth hyperbolic functions, respectively, while the second method gives the bright and singular solitons in terms of sech–csch hyperbolic functions, respectively. But in the case of quadratic-cubic law, both methods give the bright-singular solitons in terms of sech–csch hyperbolic functions, respectively, with different arguments.

Solitons and conservation laws in magneto–optic waveguides having parabolic–nonlocal law of refractive index

This paper reveals soliton solutions to magneto–optic waveguides that maintain parabolic–nonlocal law of refractive index. The unified Riccati equation expansion together with extended auxiliary equation approach together reveal bright, dark, singular as well as straddled optical solitons. These soliton solutions are obtained through a limiting process when the modulus of ellipticity approaches unity. Finally, the conservation laws are also listed.

Cubic-quartic optical soliton perturbation having four laws non-linearity with a prolific integration algorithm

New and novel solitons and other solutions to the cubic–quartic nonlinear Schrödinger's equation in a non-Kerr law media with four laws of non-linearity namely, parabolic law, quadratic–cubic law, the non-local law and weak non-local law have been found in this article. The unified Riccati equation expansion method is applied in this paper. This equation governs the propagation of solitons through nonlinear optical fibers. This yields bright, dark, singular optical solitons and other solutions that are all presented along with their respective parameter restrictions.

Exhibit of highly dispersive optical solitons in birefringent fibers with four forms of nonlinear refractive index by exp-function expansion

This paper employs exp-function scheme to obtain highly dispersive optical solitons that appear, in birefringent fibers, with four forms of nonlinear media. These are Kerr law, quadratic-cubic law, polynomial law and non-local law. The existence criteria of the solitons are also presented.

A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams

With the use of differential quadrature method (DQM), forced vibrations and resonance frequency analysis of functionally graded (FG) nano-size beams rested on elastic substrate have been studied utilizing a shear deformation refined beam theory which contains shear deformations influence needless of any correction coefficient. The nano-size beam is exposed to uniformly-type dynamical loads having partial length. The two parameters elastic substrate is consist of linear springs as well as shear coefficient. Gradation of each material property for nano-size beamhas been defined in the context of Mori-Tanaka scheme. Governing equations for embedded refined FG nanosize beams exposed to dynamical load have been achieved by utilizing Eringen's nonlocal differential law and Hamilton's rule. Derived equations have solved via DQM based on simply supported-simply supported edge condition. It will be shown that forced vibrations properties and resonance frequency of embedded FG nano-size beam are prominently affected by material gradation, nonlocal field, substrate coefficients and load factors.