Dual-power Law Nonlinearity Research Articles

Cubic–quartic optical solitons with Biswas–Milovic equation having dual-power law nonlinearity using two integration algorithms

Objective:The present paper reports cubic–quartic optical solitons with the newly introduced governing model derived from the Biswas–Milovic equation for the first time. The model is considered with dual-power nonlinear form. Methods:The modified Kudryashov’s algorithm and the addendum to Kudryashov’s approach are used. Results:Singular, bright–singular, bright and dark solitons are extracted by two integration approaches that come from the Kudryashov’s integration algorithm. Such solitons are formulated via parametric restrictions that are also indicated.

Generalized Jacobi Elliptic Solutions for the KdV Equation with Dual Power Law Non-Linearity and for the Power Law KdV-Burger Equation with the Source

Generalized Jacobi Elliptic Solutions for the KdV Equation with Dual Power Law Non-Linearity and for the Power Law KdV-Burger Equation with the Source

Lie Group Classification of Generalized Variable Coefficient Korteweg-de Vries Equation with Dual Power-Law Nonlinearities with Linear Damping and Dispersion in Quantum Field Theory

Many physical phenomena in fields of studies such as optical fibre, solid-state physics, quantum field theory and so on are represented using nonlinear evolution equations with variable coefficients due to the fact that the majority of nonlinear conditions involve variable coefficients. In consequence, this article presents a complete Lie group analysis of a generalized variable coefficient damped wave equation in quantum field theory with time-dependent coefficients having dual power-law nonlinearities. Lie group classification of two distinct cases of the equation was performed to obtain its kernel algebra. Thereafter, symmetry reductions and invariant solutions of the equation were obtained. We also investigate various soliton solutions and their dynamical wave behaviours. Further, each class of general solutions found is invoked to construct conserved quantities for the equation with damping term via direct technique and homotopy formula. In addition, Noether’s theorem is engaged to furnish more conserved currents of the equation under some classifications.

Soliton solutions for some nonlinear models in mathematical physics via conservation laws

<abstract><p>In this paper, we derive the soliton solutions from conserved quantities for the Benjamin-Bona-Mahoney equation with dual-power law nonlinearity (BBM), modified regularized long wave (MRLW) equation, modified nonlinearly dispersive KdV equations 2K(2, 2, 1) and 3K(3, 2, 2) equation, which are constructed by the multiplier approach (variational derivative method). Finally, we give the numerical simulations to illustrate this method.</p></abstract>

Langrangian formulation and solitary wave solutions of a generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity in physical sciences and engineering

This paper presents analytical studies carried out explicitly on a higher-dimensional generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity arising in engineering and nonlinear science. We obtain analytic solutions for the underlying equation via Lie group approach as well as direct integration method. Moreover, we engage the extended Jacobi elliptic cosine and sine amplitude functions expansion technique to seek more exact travelling wave solutions of the equation for some particular cases. Consequently, we secure, singular and nonsingular (periodic) soliton solutions, cnoidal, snoidal as well as dnoidal wave solutions. Besides, we depict the dynamics of the solutions using suitable graphs. The application of obtained results in various fields of sciences and engineering are presented. In conclusion, we construct conserved currents of the aforementioned equation via Noether’s theorem (with Helmholtz criteria) and standard multiplier technique through the homotopy formula.

Optical solitons in twin-core couplers with the nearest neighbor coupling

In this work, we concern with the soliton solutions to an optical twin-core coupler that occur with four sorts of nonlinearities viz. Kerr law, power law, parabolic law, and dual power-law nonlinearity. The twin-core couplers with the nearest neighbor linear coupling are considered and bright, dark, and singular optical solitons are extracted with the aid of the integration algorithm of the new mapping method. The appropriate constraint conditions are naturally emerged to secure the existence of these solitons. For physical classification of the newly acquired solutions, we have expressed them graphically to describe the physical interpretation of distinct shaped solutions more evidently.

Traveling waves in a generalized Camassa–Holm equation involving dual-power law nonlinearities

This article focuses on traveling waves including peakons, periodic peakons, compactons and solitary waves as well as the persistence of some of these waves in a generalized Camassa–Holm (gCH) equation involving dual-power law nonlinearities. Firstly, we analyze the global phase portraits of the associated traveling wave system by a dynamical system-based approach. All the traveling waves are classified and their corresponding parameter conditions are obtained. It is found that the gCH equation with dual-power law nonlinearities can admit different peakons under different parameter conditions. Secondly, we pay attention to the persistence of solitary waves, i.e., the existence of solitary waves in a perturbed gCH equation by using geometric singular perturbation theory (GSPT) and an “explicit” Melnikov method. An elementary method to calculate the unperturbed homoclinic orbits and the associated Melnikov integral in an “explicit” way is developed in this article.

Conservation laws for solitons in magneto–optic waveguides with dual–power law nonlinearity

This work recovers singular and bright solitons to magneto–optic waveguides with dual–power nonlinear form by traveling wave algorithm. Subsequently, the conservation laws are identified with multiplier scheme.

New impressive behavior of the exact solutions to the Benjamin-Bona-Mahony-Burgers equation with dual power-law nonlinearity against its numerical solution

From point of view of this work, we will establish a novelty impressive behavior to the traveling wave solutions to the Benjamin-Bona-Mahony-Burgers equation (BBMBE) with dual power-law nonlinearity which is stretch to the Korteweg-de Varies equation but has more advantages compared with it. The traveling wave solutions of this equation have been achieved for the first time in the framework of two different techniques namely the Paul-Painleve approach method (PPAM) and the Riccati-Bernoulli Sub-ODE method (RBSODM). Furthermore, the corresponding numerical solutions for all achieved exact solutions via the above two methods will be documented in the framework of the variational iteration method.

Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities

The nonlinear wave equation is a significant concern to describe wave behavior and structures. Various mathematical models related to the wave phenomenon have been introduced and extensively being studied due to the complexity of wave behaviors. In the present work, a mathematical model to obtain the solution of the nonlinear wave by coupling the classical Camassa-Holm equation and the Rosenau-RLW-Kawahara equation with the dual term of nonlinearities is proposed. The solution properties are analytically derived. The new model still satisfies the fundamental energy conservative property as the original models. We then apply the energy method to prove the well-posedness of the model under the solitary wave hypothesis. Some categories of exact solitary wave solutions of the model are described by using the Ansatz method. In addition, we found that the dual term of nonlinearity is essential to obtain the class of analytic solution. Besides, we provide some graphical representations to illustrate the behavior of the traveling wave solutions.

Exact Solutions of the KdV Equation with Dual-Power Law Nonlinearity

In this paper, we investigate the KdV equation with dual-power law nonlinearity. As a result, we have obtained general exact travelling wave soliton solutions such as bright soliton solution, dark soliton solution and periodic solution. These solutions have many free parameters in such away that they may be used to simulate many experimental situations. The main contribution in this work is to give the general solution of the obtained equations with different values of parameters $$n$$ .

New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which include hyperbolic function solutions, trigonometric function solutions, and rational function solutions, is derived by utilizing the new extendedG′/G-expansion method. By selecting appropriate parameters of the solutions, numerical simulations are presented to explain further the propagation of optical pulses in optic fibers.

Dynamical behaviors and oblique resonant nonlinear waves with dual-power law nonlinearity and conformable temporal evolution

<p style='text-indent:20px;'>In this article, the oblique resonant traveling waves and dynamical behaviors of (2+1)-dimensional Nonlinear Schrödinger equation along with dual-power law nonlinearity, and fractal conformable temporal evolution are reported. The considered equation is converted to an ordinary differential equation by taking the traveling variable wave transform and properties of Khalil's conformable derivative into account. The modified Kudryashov method is implemented to divulge the oblique resonant traveling wave of such an equation. It is found that the obliqueness is only affected on width, but not on amplitude and phase patriots of resonant nonlinear propagating wave dynamics. The research outcomes are very helpful for analyzing the obliquely propagating nonlinear resonant wave phenomena and their dynamical behaviors in several nonlinear systems having Madelung fluids and optical bullets.

New Exact Nematicon Solutions of Liquid Crystal Model With Different Types of Nonlinearities

The aim of this work is to explore and find new closed-form nematicon solutions for different nonlinearities which occur in nematic liquid crystals (NLC) along with proposing optical system application that utilizes NLC nonlinearities. In particular, Lie point symmetry method is employed to scrupulously inspect and acquire solutions for some interesting cases of nonlinearities which have not been fully examined in literature such as quadratic, generalized dual-power law, and eighth-order nonlinearities. A variety of different nematicon dynamics are observed, including bright solitons, dark solitons and periodic behaviors. The explicit solution form for each dynamical behavior is obtained and the solution dependence on model parameters is investigated. The proposed optical system enables the flexible realization of different types of NLC nonlinearities. To the best of our knowledge, this is the first time to attain explicit exact nontrivial solutions for the particular cases of generalized dual-power law and eighth-order nonlinearities.

Exact Soliton Solutions for Nonlinear Perturbed Schrödinger Equations with Nonlinear Optical Media

The nonlinear perturbed Schrödinger equations (NPSEs) with nonlinear terms as Kerr law, power law, quadratic-cubic law, and dual-power law nonlinearity media play an important role in optical fibers. In this article we implement the rational solitary wave method to study the NPSEs when nonlinear terms take some different forms. Additionally, we use the q-deformed hyperbolic function and q-deformed trigonometric function methods to study the exact solutions to NPSEs. Different kind of soliton solutions are obtained such as bright, dark, and singular periodic solutions to the NPSEs.

On the identification of nonlinear terms in the generalized Camassa-Holm equation involving dual-power law nonlinearities

The nonlinear waves constitute a significant concern in the design in order to understand wave behaviors and structures. Due to the complexity of the waves phenomenon, many mathematical models have been coming up and extensively being studied until now. In this paper, we introduce a new aspect to study a wave model by coupling of the classical Camassa-Holm equation and the BBM-KdV equation with the dual-power law nonlinearities. The new model still satisfies the fundamental energy conservative property as the original models. As we have known, the use of an efficient and accurate numerical method can be a beneficial tool for studying the wave behaviors; therefore, we aim to propose a finite difference scheme for solving the new model. A three-level finite difference technique is applied here in order to be able to design a linear scheme. The highlight of our scheme is to propose an alternative way to discretize the highly nonlinear terms. The class of analytical solutions of the model is derived and used to validate our numerical scheme. Like the design, the energy conservation law is preserved through the numerical scheme. In the context of theoretical analysis, the existence and uniqueness is analyzed based on a priori estimate. The stability and convergence of the numerical solution with second-order accuracy on both space and time are also provided under a mild restriction on the ratio of τ/h. Many comparisons of our scheme and a modification of the existing finite difference scheme are preformed, and the consequences confirm that the proposed scheme gives a significant improvement over the other. Moreover, in the numerical simulations, the faithfulness of the proposed method is validated by the pieces of evidence of depression solitary waves under the effect of the power of nonlinearities.

Propagation properties of chirped optical similaritons with dual-power law nonlinearity

Abstract We study the transmission of femtosecond light waves in an inhomogeneous dual-power law nonlinear model under the influence of self-frequency shift effect. Pulse evolution in such system is described by a generalized higher-order nonlinear Schrodinger equation incorporating the contributions of distributed self-frequency shift, dispersion, dual-power law nonlinearity, and gain/loss. As a result, a variety of analytical similaritons are derived for the first time by a similarity transformation connected to the related constant-coefficients model. We found that in the presence of self-frequency shift effect, the optical similaritons acquire a nonlinear chirp which has a power-law dependence on the intensity of the pulse. The evolution behaviors of presented chirped similaritons are also presented in two different soliton control systems.

Solitons in magneto–optic waveguides with dual–power law nonlinearity

This paper applies new ϕ6 model expansion scheme to obtain solitons in magneto–optic waveguides that come with dual–power law nonlinearity. Initially, the solutions are in terms of Jacobi's elliptic functions. Upon approaching the limiting values of the modulus of ellipticity, bright, dark and singular solitons emerge. The existence criteria of such solitons are also presented.

Optical solitons for Biswas–Milovic equation by new extended auxiliary equation method

Biswas–Milovic equation is used to narrate the nonlinear dynamics of optical solitons in nonlinear optics. With the aid of new extended auxiliary method, we find Jacobi elliptic functions solutions which degenerate to bright, dark, singular and other solitary wave solutions with Kerr law and dual power law nonlinearities.