Analytical wave solutions of an electronically and biologically important model via two efficient schemes

We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.

Nonlinear dynamical wave structures of Zoomeron equation for population models

The nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achieved for the first time in the framwork of the Paul-Painlevéapproach method(PPAM).When the variables appearing in the exact solutions take specific values,the solitary wave solutions will be easily obtained.The realized results prove the efficiency of this technique.

Interaction properties of solitons for a couple of nonlinear evolution equations

We study one-and two-soliton solutions for the Cahn–Allen(CA) equation and the Brethorton equation. The CA equation has broad spectrum of applications especially in anti-phase boundary motion and it is used in phase-field models.While the Brethorton equation is a model for dispersive wave systems, it is used to find the resonant nonlinear interaction among three linear modes. We use the Hirota bilinear method to obtain one-and two-soliton solutions to the CA equation and the Brethorton equation.

Stability analysis and soliton solutions of the(1+1)-dimensional nonlinear chiral Schrodinger equation in nuclear physics

The nonlinear Schrodinger equation equation is one of the most important physical models used in optical fiber theory to explain the transmission of an optical soliton.The field of chiral soliton propagation in nuclear physics is very interesting because of its numerous applications in communications and ultra-fast signal routing systems.The(1+1)-dimensional chiral dynamical structure that describes the soliton behaviour in data transmission is dealt with in this work using a variety of in-depth analytical techniques.This work has applications in particle physics,ionised science,nuclear physics,optics,and other applied mathematical sciences.We are able to develop a variety of solutions to demonstrate the behaviour of solitary wave structures,periodic soliton solutions,chiral soliton solutions,and bell-shaped soliton solutions with the use of applied techniques.Moreover,in order to verify the scientific calculations,the stability analysis for the observed solutions of the governing model is taken into consideration.In addition,the3-dimensional,contour,and 2-dimensional visuals are supplied for a better understanding of the behaviour of the solutions.The employed strategies are dependable,uncomplicated,and effective;yet have not been utilised with the governing model in the literature that is now accessible.The resulting outcomes have impressive applications across a large number of study areas and computational physics phenomena representing real-world scenarios.The methods applied in this model are not utilized on the given models in previous literature so we can say that these describe the novelty of the work.

On some new travelling wave structures to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model

In this article,the(1/G')-expansion method,the Bernoulli sub-ordinary differential equation method and the modified Kudryashov method are implemented to construct a variety of novel analytical solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model representing the wave propagation through incompressible fluids.The linearization of the wave structure in shallow water necessitates more critical wave capacity conditions than it does in deep water,and the strong nonlinear properties are perceptible.Some novel travelling wave solutions have been observed including solitons,kink,periodic and rational solutions with the aid of the latest computing tools such as Mathematica or Maple.The physical and analytical properties of several families of closed-form solutions or exact solutions and rational form function solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model problem are examined using Mathematica.

Investigation of soliton solutions with different wave structures to the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation

The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials.These solutions are exerted via the new extended FAN sub-equation method.We successfully obtain dark,bright,combined bright-dark,combined dark-singular,periodic,periodic singular,and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems.3D figures are illustrated under an appropriate selection of parameters.The applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena.

New Optical Soliton Solutions of the Perturbed Fokas-Lenells Equation

In this article, we employ the perturbed Fokas-Lenells equation(FLE), which represents recent electronic communications. The Riccati-Bernoulli Sub-ODE method which does not depend on the balance rule is used for thefirst time to obtain the new exact and solitary wave solutions of this equation. This technique is direct, effective and reduces the large volume of calculations.

Exact solutions of the conformable fractional EW and MEW equations by a new generalized expansion method

In this paper,we used the generalized(G’/G)-expansion method to construct exact solutions for conformable fractional nonlinear partial differential equations.This method is applied to obtain exact solutions for conformable fractional equal width wave equation(EW equation)and conformable fractional modified equal width wave equation(MEW equation).Based on the proposed method,several new exact solutions have been obtained.The proposed method is powerful and easily applicable for solving different types of conformable fractional partial differential equations.

New solitary wave and other exact solutions of the van der Waals normal form for granular materials

The investigation of exact solitary wave solutions to the nonlinear partial differential equation plays an important role to understand any physical phenomena in diverse applied fields.The current work is re-lated to the most prominent nonlinear model named as the van der Waals normal form that appeared naturally and also industrially for the granular materials.In oceanography,the sea ice,sand and snow are some examples of aforesaid matter among others.We employ two novel integration approaches named as the simplest equation method and the exp a function method to explore the above mentioned van der Waals model.As a backlash,many new solitary waves and other exact solutions are retrieved.The ob-tained results depict that the used approaches are simple and effective to deal with nonlinear models.Also,the numerical simulation of some solutions via two and three dimension graphical configurations are presented for certainty and exactness.

New-fashioned solitons of coupled nonlinear Maccari systems describing the motion of solitary waves in fluid flow

The Schrodinger equation type nonlinear coupled Maccari system is a significant equation that flourished with the wide-ranging arena concerning fluid flow and the theory of deep-water waves,physics of plasma,nonlinear optics,etc.We exploit the enhanced tanh approach and the rational(G/G)-expansion process to retrieve the soliton and dissimilar soliton solutions to the Maccari system in this study.The suggested systems of nonlinear equations turn into a differential equation of single variable through executing some operations of wave variable alteration.Thereupon,with the successful implementation of the advised techniques,a lot of exact soliton solutions are regained.The obtained solutions are depicted in 2D,3D,and contour traces by assigning appropriate values of the allied unknown constants.These diverse graphical appearances assist the researchers to understand the underlying processes of intricate phenomena of the leading equations.The individual performances of the employed methods are praise-worthy which justify further application to unravel many other nonlinear evolution equations ascending in various branches of science and engineering.

Optical solitons for the decoupled nonlinear Schr?dinger equation using Jacobi elliptic approach

Most of the important aspects of soliton propagation through optical fibers for transcontinental and transoceanic long distances can best be described using the nonlinear Schr?dinger equation.Optical solitons are electromagnetic waves that span in nonlinear dispersive media and permit the stress and intensity to stay unaltered as a result of the delicate balance between dispersion and nonlinearity effects.However,this study exploited the Jacobi elliptic method and obtained different soliton solutions of the decoupled nonlinear Schr?dinger equation with ease.Discussions about the obtained solutions were made with the aid of some 3D graphs.