Dual-power Law Research Articles

Dark, bright and singular optical solitons for Biswas–Milovic equation with Kerr and dual power law nonlinearities

This paper attains cubic-quartic optical solitons of the Biswas–Milovic equation with dual power law and Kerr law nonlinearities. Dark, bright, singular and combo-singular solitons solutions are obtained with the F-expansion method. The solutions gained in our this work are newer than the obtained solutions using different method before this work in the literature. In order to better convey the physical significance of the solutions, we also include 2D and 3D graphics. The computational software MATHEMATICA is the helping tool for visualizing and analyzing the derived solutions.

Noether symmetries, group analysis and soliton solutions of a (3+1)-dimensional generalized fifth-order Zakharov–Kuznetsov model with power, dual power laws and dispersed perturbation terms with real-world applications

Highly important is a three-dimensional nonlinear partial differential equation because for many physical systems, one can, subject to suitable idealizations, formulate a differential equation that describes how the system changes in time. Thus, this article comprehensively reveals the investigation carried out on a (3+1)-dimensional generalized fifth-order Zakharov–Kuznetsov equation with power-law as well as dual power-law nonlinearities analytically, where the fifth-order term involved is regarded as a dispersion perturbation term. We utilize the well-celebrated Noether’s theorem to comprehensively construct conserved currents of the underlying equation. A detailed Lie group analysis of the understudied model consisting of power-law nonlinearities is further performed. This involves performing reductions of the underlying models using their Lie point symmetries. In consequence, various invariants are found. In addition, the equation reduces to diverse ordinary differential equations using its point symmetries and consequently diverse solutions of interest were achieved. Moreover, we derive some solitary wave solutions by invoking the newly introduced logistic function technique for some particular cases of the equation under consideration. In consequence, we achieve some exponential function solutions. In addition, the physical meaning of the results is put on the front burner by revealing the wave dynamics of these solutions via graphical depictions. Finally, the significance of the robust and detailed findings in the work are further corroborated with various real-world applications.

New optical soliton solutions to nonlinear Schrödinger equation with fractional temporal evolution having parabolic and dual power law nonlinearities

New optical soliton solutions to nonlinear Schrödinger equation with fractional temporal evolution having parabolic and dual power law nonlinearities

Analytical and numerical studies of the modified Kawahara equation with dual-power law nonlinearities

Analytical and numerical studies of the modified Kawahara equation with dual-power law nonlinearities

Novel solution structures localized in fractional integrable coupled nonlinear Schrödinger equations

Fractional calculus highlights its importance and has been expanded to many fields. This paper focuses on fractional integrable systems and their novel structural solutions to comply with the forefront development of nonlinear waves. Specifically, a system of fractional integrable coupled nonlinear Schrödinger (CNLS) equations are first derived from the associated linear spectral problem equipped with space-time conformable fractional derivatives of different orders. Then, by extending Darboux transformation (DT) and its generalized version to the derived fractional CNLS equations, we obtained fractional single-soliton solutions and double- and triple-semirational solutions that obey the dual power laws of independent variables. Under the dominant influences of space-time fractional orders, some novel solution structures are finally revealed based on the obtained solutions. In terms of characteristics, these spatial structures exhibit inclination, symmetry and spikes. Observing from the perspective of propagation, some of these obtained solutions have time-varying velocities and widths. From the perspective of spatiotemporal structures, some solutions form collapsed quadrangular pyramids. All of these novel solution structures cannot be supported by the integer-order CNLS equations.

Management of soliton pulse speed in inhomogeneous optical waveguides with dual-power law refractive index

Management of soliton pulse speed in inhomogeneous optical waveguides with dual-power law refractive index

Exact Solutions of Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-Law Nonlinearity by Modified Exp-Function Method

In this work, the Benjamin-Bona-Mahoney-Burgers equation has been examined, which includes the dual power-law nonlinearity and diffraction term. By using the modified exp-function method, the exact solutions of the governing equation have been obtained. The resulting traveling wave solutions have been found to exhibit various characteristics, such as being dark solitons, periodic, and singular, depending on the values of certain constants. To further illustrate these solutions, 3D, 2D, and contour graphs have been displayed. To the best of our knowledge, this is the first time in literature that the dark solitons, periodic soliton, and singular soliton solutions of considered equations have been obtained by utilizing the modified exp-function method.

Propagation of chirped optical solitons for perturbation higher order nonlinear Schrödinger equation with dual-power law nonlinearity by [formula omitted] expansion method

New exact solutions for the perturbation higher order nonlinear Schrödinger equation (NLSE) with dual-power law nonlinearity are investigated using the ϕ6 expansion method. This type of NLSE models the propagation of femtosecond pulses in fiber optics which has many applications such as infrared time-resolved spectroscopy, ultrahigh-bit-rate optical communication systems and ultrafast optics. The application of ϕ6 expansion technique provided many different types of solutions. Dark solitons, bright solitons, singular solitons, hyperbolic solutions, periodic and singular periodic solutions are obtained. The graphical representations of some selected solutions are provided to present both the dynamical behavior of solutions and the effect of changing the nonlinearity degree on their dynamical behavior. This study concludes that the nonlinearity degree controls the dynamical behavior of the light pulse.

Construction of solitons in nano optical fibers with dual-power law nonlinearity using MEDAM

Construction of solitons in nano optical fibers with dual-power law nonlinearity using MEDAM

Exact Solutions of Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-Law Nonlinearity by Modified Exp-Function Method

In this work, the Benjamin-Bona-Mahoney-Burgers equation is examined which includes the dual power law nonlinearity and diffraction term. The exact solutions of governing equation are obtained by exploting the modified exp-function method. For some specific values of constants, the obtained travelling wave soluions are dark soliton, periodic and singular in nature. Also, 3-D, 2-D and contour graphical representations of obtained solutions are displayed.

Exact Solutions of Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-Law Nonlinearity by Modified Exp-Function Method

In this work, the Benjamin-Bona-Mahoney-Burgers equation is examined which includes the dual power law nonlinearity and diffraction term. The exact solutions of governing equation are obtained by exploting the modified exp-function method. For some specific values of constants, the obtained travelling wave soluions are dark soliton, periodic and singular in nature. Also, 3-D, 2-D and contour graphical representations of obtained solutions are displayed.

Chirped optical solitons of the perturbed resonant nonlinear Schrödinger equation with dual-power law nonlinearity

Chirped optical solitons of the perturbed resonant nonlinear Schrödinger equation with dual-power law nonlinearity

Optical solitons of the complex Ginzburg-Landau equation having dual power nonlinear form using $\varphi^{6}$-model expansion approach

This paper employs a novel $\varphi ^{6}$-model expansion approach to get dark, bright, periodic, dark-bright, and singular soliton solutions to the complex Ginzburg-Landau equation with dual power-law non-linearity. The dual-power law found in photovoltaic materials is used to explain nonlinearity in the refractive index. The results of this paper may assist in comprehending some of the physical effects of various nonlinear physics models. For example, the hyperbolic sine arises in the calculation of the Roche limit and the gravitational potential of a cylinder, the hyperbolic tangent arises in the calculation of the magnetic moment and the rapidity of special relativity, and the hyperbolic cotangent arises in the Langevin function for magnetic polarization. Frequency values, one of the soliton's internal dynamics, are used to examine the behavior of the traveling wave. Finally, some of the obtained solitons' three-, two-dimensional, and contour graphs are plotted.

Investigations of bright, dark, kink-antikink optical and other soliton solutions and modulation instability analysis for the (1+1)-dimensional resonant nonlinear Schrödinger equation with dual-power law nonlinearity

Investigations of bright, dark, kink-antikink optical and other soliton solutions and modulation instability analysis for the (1+1)-dimensional resonant nonlinear Schrödinger equation with dual-power law nonlinearity

Comparative study of the accuracy of friction factor correlations developed for flow of inelastic yield power-law fluids in pipes

An extensive review of the friction factor correlations used for pressure loss prediction of yield power-law (YPL) fluid flow in pipes has been conducted, and the results are summarized in this paper.A comparative study was also conducted to determine the predictive performances of various laminar and turbulent friction factor models developed for YPL fluid flow in pipes. Model predictions of frictional pressure losses were validated by comparing them with the experimentally measured pressure drop data obtained from the flow of several YPL fluids in pipes.Investigations were further extended to determine the impact of the variation of YPL fluid rheological characteristics (resulting from using different rheological characterization methods) on the pressure drop predictions.A wide range of generalized Reynolds numbers (i.e., 20 to 9000, as defined by the API-RP:13D) in a pipe flow configuration was considered in the analyses. The yield stress of the test fluids (determined by using the nonlinear curve fitting technique recommended by the API RP:13D) varied from 0.10 to 0.95 Pa.The results indicated that Hanks and Ricks' model predicted the pressure drop of YPL fluid flow in pipes better than any other models, both in laminar and turbulent flow regimes, matching the experimental data within a ±10% error range.Variations of the YPL model parameters (resulting from using different rheological characterization methods) significantly impacted the pressure drop predictions. Using YPL model parameters obtained from the non-iterative dual power law (DPL) approximation method (as recommended by API-RP:13D) and Hanks and Ricks' model yielded the most accurate pressure drop predictions for the pipe flow of YPL fluids.

Investigation of chirped optical solitons perturbation of higher order NLSE via improved modified extended tanh function approach

This context focuses on examining the manner in which localized waves travel through a non-linear medium that adheres to a dual-power law. This medium encompasses a range of disruptions like inter modal dispersion, self frequency shift, and self-steepening effects. This investigation entails employing an improved modified extended tanh function (IMETF) technique to obtain various novel optical soliton solutions which include bright, dark, singular and combo singular-dark solitons. Furthermore, we extract singular periodic, exponential, rational, and Weierstrass elliptic solutions. To showcase their physical characteristics, we provide graphical representations in 3D and 2D of some of the derived solutions.

Grey-Black Optical Solitons, Homoclinic Breather, Combined Solitons via Chupin Liu’s Theorem for Improved Perturbed NLSE with Dual-Power Law Nonlinearity

In this article, we consider the improved perturbed nonlinear Schrödinger Equation (IP-NLSE) with dual power law nonlinearity, which arises in optical fibers and photovoltaic-photo-refractive materials. We found grey and black optical solitons of the governing equation by means of a suitable complex envelope ansatz solution. By using the Chupin Liu’s theorem (CLT) for the grey and black solitons, we evaluated new categories of combined optical soliton (COS) solutions to the IP-NLSE. The propagation behaviors for homoclinic breathers (HB), multiwaves and M-shape solitons will be analytically examined. All new analytical solutions will be found by an ansatz function scheme and suitable transformations. Multiwave solitons have been reported by using a three-waves technique. Furthermore, two kinds of interactions for M-shape soliton through exponential functions will be examined.

Optical Soliton Perturbation with Parabolic Law Nonlinearity

This paper recovers a broad spectrum of optical solitons for the perturbed nonlinear Schrödinger’s equation having a dual-power law of nonlinearity. The perturbation terms are from inter-modal dispersion and self-frequency shift. The integration scheme is the improved extended tanh function approach. The parameter constraints that naturally emerge are also enumerated.

Dispersive optical solitons and conservation laws of Radhakrishnan–Kundu–Lakshmanan equation with dual–power law nonlinearity

The current paper implements three elegant approaches to recover a complete spectrum of optical solitons to the Radhakrishnan–Kundu–Lakshmanan equation with dual–power law of nonlinear refractive index. The conservation laws are also recovered by the usage of multipliers approach. The parameter constraints for the existence of such solitons are also enumerated. The numerical simulations of the recovered soliton solutions are also presented.

An energy-preserving finite difference scheme with fourth-order accuracy for the generalized Camassa–Holm equation

In this article, an energy-preserving finite difference scheme for solving the generalized Camassa–Holm (gCH) equation with the dual-power law nonlinearities is proposed. We first show that the solution of the initial–boundary-value gCH equation is unique and continuously dependent on the initial condition, then we construct a linear energy-preserving difference scheme for the gCH equation. The proposed difference scheme is three-level implicit, and the numerical convergence order is O(τ2+h4). The energy conservation, unique solvability, convergence and stability of the finite difference scheme are rigorously proved by using the discrete energy method. Finally, some numerical examples show that the proposed numerical scheme is efficient and reliable.