Abundant Exact Traveling Wave Solutions of the (2+1)-Dimensional Couple Broer-Kaup Equations

To describe the propagation of small amplitude waves in nonlinear dispersive media, it is frequently necessary to take account of dissipative mechanisms to perfectly reflect real situations in many branches of physics like plasma physics, fluid dynamics and nonlinear optics. In this paper, the exp(-Fi(Eta))-expansion method is employed to solve the (2+1)-Dimensional couple Broer-Kaup equations as a model for wave propagation in nonlinear media with dispersive and dissipative effects. As a result, a number of exact traveling wave solutions including solitary wave and periodic wave have been found for the equation. Some representative 3D profiles and 2D profiles for different values of variables of the wave solutions are graphically displayed and discussed

Characteristics of Pulsatile Blood Flow Through 3-D Geometry of Arterial Stenosis

AbstractA numerical simulation is carried out to demonstrate the significant changes of flow behaviour for two different severities of arterial stenosis. Two stenosis levels of 65% and 85% are considered by area. The blood is considered as flowing fluid and assumed to be incompressible, homogeneous and Newtonian, while artery is assumed to be a rigid wall. The transient analysis is performed using ANSYS-14.5. The flow pattern, wall shear stress (WSS), pressure contours, and Centre-line velocity distribution are observed at early-systole, peak-systole and diastole for better understanding of arterial disease. Wall Share Stress distribution shows that as severity increases, sharing of flow also increases for all cases. Thus maximum stress is exerted in throat region at peak systole. The pressure distribution demonstrates that at all cases 85% stenotic artery creates more force than 65% stenotic artery at their pre-stenotic region. Interestingly, a recirculation region is visible at the post stenotic region in 85% stenotic artery for all cases and recirculation region increases with the decrease of the inlet flow velocity. Analysis indicates that the significant flow changes happen in the post stenotic region

Bilinear form of the regularized long wave equation and its multi-soliton solutions

We consider utmost significant model, namely, the regularized long-wave equation involving dispersion and weedy nonlinearity effects that arises in the nonlinear dynamics of phonon packets in crystals, shallow water, plasma and ion acoustic waves. The Hirota direct approach has been used to deform the model into its bilinear representation. We derive one, two and three solitons solutions from the bilinear form. Moreover, a general formula of N-solitons solution is given of the model. Graphical representations of the achieved solutions are given and found elastic interaction situation of the solitons

New soliton solutions and modulation instability analysis of the regularized long-wave equation in the conformable sense

In this manuscript, we explore the solitary soliton of the regularized long-wave (RLW) equation which involving with weedy nonlinearity effects and dispersion relations which arises in shallow water, phonon packets in crystals, plasma wave and ion auditory waves. To execute the soliton solutions, we applied the advance Exp( − φ(ξ)) expansion method and the new form of modified Kudryashov's technique with conformable derivative from the fractional RLW model. For the explanation of the nature of RLW model, we obtained some behavior such as on the obtained solitons as bell-wave, rogue wave, periodic and double-periodic waves. This article offered the effects of conformable derivative to check the stability of the obtained phenomena. To check the stability of this model, we use the modulation instability analysis also. This work has a decent sense to endorse the extensive proposal of the model. Some 3-D and 2-D plots with their graphical explanation provides this research to characterized the obtained waves of RLW model

Variable coefficient exact solution of Sharma–Tasso–Olver model by enhanced modified simple equation method

This article presents variable coefficients solution in the form of soliton, bell shape solution, periodic solution, parabolic periodic soliton of Sharma–Tasso–Olver equation which fundamentally apply to the fission and fusion mechanism of particle in nuclear physics. Solitary wave takes the leading position in electromagnetic field, atomic quantum theory, theoretical relativistic relation etc. The enhanced modified simple equation (EMSE) method is used to generalize solitary wave solutions for Sharma–Tasso–Olver (STO) equation. The computational software maple 18 is used to derive the corresponding results in the 3D plot, density plot and counter plots for the different types of time function used in EMSE scheme

Optical solitons to the fractional order nonlinear complex model for wave packet envelope

This research deals with the fractional order nonlinear complex model, which is a general form of nonlinear Schrodinger equation. This model demonstrates boson gas among 2 as well as 3 body collisions, nuclear hydro-dynamics allied with Skyrme energies, in addition the optical rhythm propagations within dielectric non-Kerr media. To analyze and generate complex dynamics, optical soliton solutions of the model are derived through improved generalized Riccati equation mapping scheme. As a result, bright, dark and combo bright-dark optical wave envelopes and oscillating pulse bright optical solitons are obtained. The effects of fractionality and parameters are also illustrated with few numerical graphics of the achieved results. The achieved optical (bright and dark) solitons solutions can be used in signal transmission through optical fiber communications system