Jacobi Elliptic Function Expansion Method Research Articles

Optical solitons in birefringent fibers with Biswas–Arshed model by generalized Jacobi elliptic function expansion method

In this paper, we employ a generalized Jacobi elliptic function expansion method to extract optical solitons and other solutions to Biswas–Arshed model in birefringent fibers. Jacobi elliptic functions solutions, bright solitons, singular solitons, dark solitons, periodic wave solutions and other solutions have been found.

Optical solitons and other solutions in birefringent fibers with Biswas-Arshed equation by Jacobi's elliptic function approach

In this paper, the Jacobi elliptic function expansion method is applied to construct optical solitons and other solutions of the newly proposed Biswas-Arshed equation in birefringent fibers witch involving two component form for vector solitons. Besides dark and bright solitons, Jacobi elleptic periodic type solutions and hyperbolic function solutions are also obtained as a byproduct.

A novel method for new solutions of time fractional (1+2)-dimensional nonlinear Schrödinger equation involving dual-power law nonlinearity

In this paper, a novel method has been used to solve time fractional [Formula: see text]-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity. Using the newly-proposed Jacobi elliptic function expansion method, new double periodic, bright and soliton solutions of the aforesaid equation have been obtained. The results show that the proposed method is a convenient, efficient and straightforward technique to devise new soliton solutions of the presently-mentioned equation.

Dispersive and propagation of shallow water waves as a higher order nonlinear Boussinesq-like dynamical wave equations

The propagation of small amplitude long capillary–gravity waves on the surface of shallow water described by the higher order nonlinear Boussinesq type wave equation. This model is arising in mathematical physics, shallow water waves, fluid dynamics and fluid flow. We applied the modified Jacobi elliptic function expansion method to obtained exact solutions in the type of solitary wave and elliptic functions solutions. These solutions helps the mathematicians and physicians to understand the physical phenomena of this model. This technique can be utilized on other models to launch further exclusively novel solutions for other categories of nonlinear PDEs occurring in mathematical Physics.

New Analytical Solutions for Time Fractional Benjamin-Ono Equation Arising Internal Waves in Deep Water

In this article, the author sets up the abundant traveling wave solutions for time fractional Benjamin-Ono equation which was introduced to describe internal waves in stratified fluids by using Jacobi elliptic function expansion method. The traveling wave solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. It can be seen that the obtained results are found to be important for the statement of some physical demonstrations of problems in mathematical physics and ocean engineering. In ocean engineering Benjamin-Ono equations are generally used in computer simulation for the water waves in deep water and open seas.

Jacobi Elliptic Function Expansion Method for Solving KdV Equation with Conformable Derivative and Dual-Power Law Nonlinearity

In this work, the KdV equation with conformable derivative and dual-power law nonlinearity is considered. It is exceedingly used as a model to depict the feeble nonlinear long waves in different fields of sciences. Furthermore, it explains the comparable effects of weak dispersion and weak nonlinearity on the evolvement of the nonlinear waves. Using the Jacobi elliptic function expansion method, new exact solutions of that equation have been found. As results, some obtained solutions behave as periodic traveling waves, bright soliton, and dark soliton.

Nonlinear Schrödinger equation for envelope Rossby waves with complete Coriolis force and its solution

The physical features of the equatorial envelope Rossby waves including with complete Coriolis force and dissipation are investigated analytically. Staring with a potential vorticity equation, the wave amplitude evolution of equatorial envelope Rossby waves is described as a nonlinear Schrodinger equation by employing multiple scale analysis and perturbation expansions. The equation is more suitable for describing envelope Rossby solitary waves when the horizontal component of Coriolis force is stronger near the equator. Then, based on the Jacobi elliptic function expansion method and trial function method, the classical Rossby solitary wave solution and the corresponding stream function of the envelope Rossby solitary waves are obtained, respectively. With the help of these solutions, the effect of dissipation and the horizontal component of Coriolis parameter are discussed in detail by graphical presentations. The results reveal the effect of the horizontal component of Coriolis force and dissipation on the classical Rossby solitary waves.

New periodic wave solutions of a time fractional integrable shallow water equation

In this paper, author employed Jacobi elliptic function expansion method to build the new wave solutions of time fractional modified Camassa–Holm equation which is completely integrable dispersive shallow-water equation. In ocean engineering, Camassa–Holm equation is generally used as a tool in computer simulation of the water waves in shallow sees, coastal and harbors. The obtained solutions show that the Jacobi elliptic function expansion method (JEFEM) which based on Jacobi elliptic functions is an efficient, reliable, applicable and accurate tool for analytic approximation of a wide variety of nonlinear conformable time fractional partial differential equations.

New Jacobi elliptic function solutions, solitons and other solutions for the (2 + 1)-dimensional nonlinear electrical transmission line equation

In this work, we use the new Jacobi elliptic function expansion method to find exact soliton solutions for a discrete nonlinear electrical transmission line in (2 + 1) dimension. Several new solutions have been obtained. The solutions found by the current method are of varied types and include hyperbolic and trigonometric solutions, as well as Jacobi elliptic solutions. We show that the existence of these solutions depends on the parameters of the network. Comparisons of our new results with the well-known results are obtained. The solutions found here may be also used in optical fibers to transport information. The method applied here is very simple and concise and can be also applied to other nonlinear partial differential equations.

Solitons and other solutions of the nonlinear fractional Zoomeron equation

In order to investigate the nonlinear fractional Zoomeron equation, we propose three methods, namely the Jacobi elliptic function rational expansion method, the exponential rational function method and the new Jacobi elliptic function expansion method. Many kinds of solutions are obtained and the existence of these solutions is determined. For some parameters, these solutions can degenerate to the envelope shock wave solutions and the envelope solitary wave solutions. A comparison of our new results with the well-known results is made. The methods used here can also be applicable to other nonlinear partial differential equations. The fractional derivatives in this work are described in the modified Riemann–Liouville sense.

New analytical solutions of the space fractional KdV equation in terms of Jacobi elliptic functions

In this study, new families of analytical exact solutions of the space fractional Korteweg-de Vries (KdV) equation are presented. Here, the fractional derivative is considered in conformable sense. By utilizing the Jacobi elliptic function expansion method, the solutions are obtained in general form containing the hyperbolic, trigonometric, and rational functions. Also, the complex valued solutions are obtained and some solutions of this equation are demonstrated.

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

Abstract In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

Optical solitons, nonlinear self-adjointness and conservation laws for Kundu–Eckhaus equation

In this article, Kundu–Eckhaus equation (KE) is studied from the perspective of modified tanh-coth method (MTC), extended Jacobi elliptic function expansion method (EJEF), Lie symmetry analysis, nonlinear self-adjointness and conservation laws (Cls). New soliton solutions like combined dark-bright, dark, periodic wave and singular soliton solutions are obtained. The equation is found to be a nonlinear self-adjoint, we construct the Cls using the new conservation theorem presented by Ibragimov. Physical interpretation for some of the obtained solutions are illustrated in Figures.

Exact solutions for the Wick-type stochastic Kersten-Krasil’shchik coupled KdV-mKdV equations

In this article, exact solutions of Wick-type stochastic Kersten-Krasil’shchik coupled KdV-mKdV equations have been obtained by using the Jacobian elliptic function expansion method. We have used the Hermite transform for transforming the Wick-type stochastic Kersten-Krasil’shchik coupled KdV-mKdV equation into a deterministic partial differential equation. Also, we have applied the inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space.

The investigation of soliton solutions of the coupled sine-Gordon equation in nonlinear optics

The coupled sine-Gordon equation, which can be used to describe the propagation of an optical pulse in fibre waveguide, has been investigated analytically. The hyperbolic and trigonometric function solutions are constructed by the extended expansion method, and then the Jacobi elliptic, hyperbolic and trigonometric function solutions are derived with the help of the extended Jacobi elliptic function expansion method.

Soliton solutions for Davydov solitons in α-helix proteins

The propagation equation for describing Davydov solitons in α-helix proteins has been investigated analytically. There are seven integration tools to extract analytical soliton solutions. They are the Ricatti equation expansion approach, ansatz scheme, improved extended tanh-equation method, the extend exp(−Ψ(τ))-expansion method, the extended Jacobi elliptic function expansion method, the extended trial equation method and the extended G'/G− expansion method.

Explicit solitons in the parabolic law nonlinear negative-index materials

This paper deals with the existence of explicit ultra-short solitons in the negative-index materials with third-order dispersion and higher-order nonlinearities. Four integration algorithms, that are the improved modified extended tanh-function method, the extended trial equation method, the extended Jacobi elliptic function expansion method and the \(\exp \left( -\Phi \left( \eta \right) \right) \)-expansion method, are employed to extract analytical traveling wave solutions. The presented results show that exact solitons can exist in this physical model.

Extended Jacobian Elliptic Function Expansion Method and Its Applications in Mathematical Physics

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to some nonlinear evolution equations which play an important role inmathematical physics.

New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method

In this paper, the Jacobi elliptic function expansion method is proposed for the first time to construct the exact solutions of the time conformable fractional two-dimensional Boussinesq equation and the combined KdV-mKdV equation. New exact solutions are found. This method is based on Jacobi elliptic functions. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.

New solitary solutions in FPU-β atom chain

Solitons in one-dimensional FPU-[Formula: see text] lattice chains were studied by the Jacobi elliptic function expansion method under the condition of quasi-continuum approximation. It is found that there exhibits a novel nonlinear elementary excitation, i.e. exact solitary solutions. On the basis of the above, the influence of the nonlinear intensity on the solitons was analyzed. It is found that the modulation amplitude of soliton is related closely to the nonlinear parameter also.