Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(ξ))-Expansion Method

In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.

Exact Traveling Wave Solutions of Nano-Ionic Solitons and Nano-Ionic Current of MTs Using the exp(-φ (ξ ))-Expansion Method

In this work, the exp(-φ (ξ )) -expansion method is used for the first time to investigate the exact traveling wave solutions involving parameters of nonlinear evolution equations. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. The validity and reliability of the method are tested by its applications to Nano-ionic solitons wave’s propagation along microtubules in living cells and Nano-ionic currents of MTs which play an important role in biology.

Novel traveling wave solutions and stability analysis of perturbed Kaup-Newell Schrodinger dynamical model and its applications

We study the traveling wave and other solutions of the perturbed Kaup-Newell Schrodinger dynamical equation that signifies long waves parallel to the magnetic field.The wave solutions such as bright-dark(solitons),solitary waves,periodic and other wave solutions of the perturbed Kaup-Newell Schrodinger equation in mathematical physics are achieved by utilizing two mathematical techniques,namely,the extended F-expansion technique and the proposed exp(-φ(ξ))-expansion technique.This dynamical model describes propagation of pluses in optical fibers and can be observed as a special case of the generalized higher order nonlinear Schrodinger equation.In engineering and applied physics,these wave results have key applications.Graphically,the structures of some solutions are presented by giving specific values to parameters.By using modulation instability analysis,the stability of the model is tested,which shows that the model is stable and the solutions are exact.These techniques can be fruitfully employed to further sculpt models that arise in mathematical physics.

Adequate Closed Form Wave Solutions to the Generalized KdV Equation in Mathematical Physics

In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the exp(-φ(ε))-expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Solitary wave solutions for the generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation

In this paper,we utilize the exp(−ϕ(ξ))-expansion method to find exact and solitary wave solutions of the generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation.The generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation describes the model for the propagation of long waves that mingle with nonlinear and dissipative impact.This model is used in the analysis of the surface waves of long wavelength in hydro magnetic waves in cold plasma,liquids,acoustic waves in harmonic crystals and acoustic-gravity waves in compressible fluids.By using this method,seven different kinds of traveling wave solutions are successfully obtained for this model.The considered method and transformation techniques are efficient and consistent for solving nonlinear evolution equations and obtain exact solutions that are applied to the science and engineering fields.

Dispersive Solitary Wave Solutions of Strain Wave Dynamical Model and Its Stability

In the materials of micro-structured, the propagation of wave modeling should take into account the scale of various microstructures. The different kinds solitary wave solutions of strain wave dynamical model are derived via utilizing exp(-φ(ξ))-expansion and extended simple equation methods. This dynamical equation plays a key role in engineering and mathematical physics. Solutions obtained in this work include periodic solitary waves, Kink and antiKink solitary waves, bell-shaped solutions, solitons, and rational solutions. These exact solutions help researchers for knowing the physical phenomena of this wave equation. The stability of this dynamical model is examined via standard linear stability analysis, which authenticate that the model is stable and their solutions are exact. Graphs are depicted for knowing the movements of some solutions. The results show that the current methods, by the assist of symbolic calculation, give an effectual and direct mathematical tools for resolving the nonlinear problems in applied sciences.