Dual-power Law Nonlinearity Research Articles

Optical solitons and modulation instability analysis for the generalized resonant dispersive nonlinear Schrödinger equation with dual power-law nonlinearity

Optical solitons and modulation instability analysis for the generalized resonant dispersive nonlinear Schrödinger equation with dual power-law nonlinearity

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.

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

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

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.

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.

Derivation of new optical solitons for Biswas-Milovic equation with dual-power law nonlinearity using improved modified extended tanh-function method

Cubic-quartic optical solitons and other solutions for Biswas-Milovic equation with dual-power law nonlinearity are investigated using improved modified extended tanh-function method. Bright soliton solutions, dark soliton solutions, singular soliton solutions, singular periodic solutions, Jacobi elliptic solutions and hyperbolic solutions are extracted. Furthermore, some selected solutions are described graphically to demonstrate the physical nature of obtained solutions.

Solitary wave solutions to Gardner equation using improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method

<abstract><p>In this study, the improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.</p></abstract>

Chaotic Behavior of the Zakharov-Kuznetsov Equation with Dual-Power Law and Triple-Power Law Nonlinearity

The main idea of this paper is to study the chaotic behavior of Zakharov–Kuznetsov equation with perturbation. By taking the traveling wave transformation, we transform the perturbed Zakharov–Kuznetsov equation with dual-power law and triple-power law nonlinearity into planar dynamic systems, and then analyze how the external perturbed terms affect the chaotic behavior. We emphasize here that there is no chaotic phenomenon for the non-perturbed ZK equation, thus it is only caused by the external perturbed terms.

Implementation of the Exp-function approach for the solution of KdV equation with dual power law nonlinearity

Implementation of the Exp-function approach for the solution of KdV equation with dual power law nonlinearity

Dispersive optical solitons with Biswas–Milovic equation having dual-power law nonlinearity and multiplicative white noise via Itô calculus

Object:The present paper reports for the first time, dispersive optical solitons with Biswas–Milovic equation having dual-power law nonlinearity and multiplicative white noise in the Itô sense. Methods:The utilized schemes here are the new mapping approach and the addendum to Kudryashov’s algorithm. Results:Dark solitons, bright solitons, singular solitons, combo-singular solitons, combo bright-singular solitons are yielded for the proposed equation.