Exact and explicit traveling wave solutions to two nonlinear evolution equations which describe incompressible viscoelastic Kelvin-Voigt fluid

A variety of soliton solutions of time M-fractional: Non-linear models via a unified technique

This work explores diverse novel soliton solutions of two fractional nonlinear models, namely the truncated time M-fractional Chafee-Infante (tM-fCI) and truncated time M-fractional Landau-Ginzburg-Higgs (tM-fLGH) models. The several soliton waves of time M-fractional Chafee-Infante model describe the stability of waves in a dispersive fashion, homogeneous medium and gas diffusion, and the solitary waves of time M-fractional Landau-Ginzburg-Higgs model are used to characterize the drift cyclotron movement for coherent ion-cyclotrons in a geometrically chaotic plasma. A confirmed unified technique exploits soliton solutions of considered fractional models. Under the conditions of the constraint, fruitful solutions are gained and verified with the use of the symbolic software Maple 18. Keeping special values of the constraint, this inquisition achieved kink shape, the collision of kink type and lump wave, the collision of lump and bell type, periodic lump wave, bell shape, some periodic soliton waves for time M-fractional Chafee-Infante and periodic lump, and some diverse periodic and solitary waves for time M-fractional Landau-Ginzburg-Higgs model successfully. The required solutions in this work have many constructive descriptions, and corporal behaviors have been incorporated through some abundant 3D figures with density plots. We compare the m-fractional derivative with the beta fractional derivative and the classical form of these models in two-dimensional plots. Comparisons with others' results are given likewise.

Mechanical study of blood flow through a permeable capillary with slippery wall

This research presents the mechanical behavior of blood flow through capillary having smooth inner surface. In this study modelling of blood flow via permeable and lubricated capillary caused by nutrients re-absorption has been done by the help of laws of momentum and mass. The nutrients re-absorption is assumed to be constant and inner walls of the capillary are smooth and slippery therefore slip condition on the velocity and constant rate in vertical direction at the wall has considered. The Kelvin Voigt model is employed to simulate blood flow via capillaries, and results for pressure, blood flow pattern, and shear force necessary for blood flow are discovered by recursive approach. Numerical results for nutrient re-absorption from the blood and impact of smooth and slippery surfaces on blood flow are shown through graphs. The novelty of the research invents that the smoothness and slickness of capillary wall is a crucial presumption to examine the blood as non-Newtonian fluid via capillary.

Bifurcation analysis on ion sound and Langmuir solitary waves solutions to the stochastic models with multiplicative noises

This article explores on a stochastic couple models of ion sound as well as Langmuir surges propagation involving multiplicative noises. We concentrate on the analytical stochastic solutions including the travelling and solitary waves by using the planner dynamical systematic approach. To apply the method, First effort is to convert the system of equations into the ordinary differential form and present it in form of a dynamic structure. Next analyze the nature of the critical points of the system and obtain the phase portraits on various conditions of the corresponding parameters. The analytic solutions of the system in an account of distinct energy states for each phase orbit are performed. We also show how the results are highly effective and interesting to realize their exciting physical as well as the geometrical phenomena based on the demonstration of the stochastic system involving ion sound as well as Langmuir surges. Descriptions of effectiveness of the multiplicative noise on the obtained solutions of the model, and its corresponding figures are demonstrated numerically.

The modified extended tanh technique ruled to exploration of soliton solutions and fractional effects to the time fractional couple Drinfel'd-Sokolov-Wilson equation

The modified extended tanh technique is used to investigate the conformable time fractional Drinfel'd-Sokolov-Wilson (DSW) equation and integrate some precise and explicit solutions in this survey. The DSW equation was invented in fluid dynamics. The modified extended tanh technique executes to integrate the nonlinear DSW equation for achieve diverse solitonic and traveling wave envelops. Because of this, trigonometric, hyperbolic and rational solutions have been found with a few acceptable parameters. The dynamical behaviors of the obtained solutions in the pattern of the kink, bell, multi-wave, kinky lump, periodic lump, interaction lump, and kink wave types have been illustrated with 3D and density plots for arbitrary chose of the permitted parameters. By characterizing the particular benefits of the exemplified boundaries by the portrayal of sketches and by deciphering the actual events, we have laid out acceptable soliton plans and managed the actual significance of the acquired courses of action. New precise voyaging wave arrangements are unambiguously gained with the aid of symbolic computation using the procedures that have been announced. Therefore, the obtained outcomes expose that the projected schemes are very operative, easier and efficient on realizing natures of waves and also introducing new wave strategies to a diversity of NLEEs that occur within the engineering sector.

Dynamical interaction of solitary, periodic, rogue type wave solutions and multi-soliton solutions of the nonlinear models

This study presents a modification form of modified simple equation method, namely new modified simple equation method. Multiple waves and interaction of soliton solutions of the Phi-4 and Klein-Gordon models are investigated via the scheme. Consequently, we derive various novels and more general interaction, and multiple wave solutions in term of exponential, hyperbolic, and trigonometric, rational function solutions combining with some free parameters. Taking special values of the free parameters, interaction of two dark bells, interaction of two bright bells, two kinks, two periodic waves, kink and soliton, kink-rogue wave solutions are obtained which is the key significance of this method. Properties of the achieved solutions have many useful descriptions of physical behavior, correlated to the solutions are attained in this work through plentiful 3D figures, density plot and 2D contour plots. The results derived may increase the prospect of performing significant experimentations and carry out probable applications.

Explore Optical Solitary Wave Solutions of the kp Equation by Recent Approaches

The study of nonlinear evolution equations is a subject of active interest in different fields including physics, chemistry, and engineering. The exact solutions to nonlinear evolution equations provide insightful details and physical descriptions into many problems of interest that govern the real world. The Kadomtsev–Petviashvili (kp) equation, which has been widely used as a model to describe the nonlinear wave and the dynamics of soliton in the field of plasma physics and fluid dynamics, is discussed in this article in order to obtain solitary solutions and explore their physical properties. We obtain several new optical traveling wave solutions in the form of trigonometric, hyperbolic, and rational functions using two separate direct methods: the (w/g)-expansion approach and the Addendum to Kudryashov method (akm). The nonlinear partial differential equation (nlpde) is reduced into an ordinary differential equation (ode) via a wave transformation. The derived optical solutions are graphically illustrated using Maple 15 software for specific parameter values. The traveling wave solutions discovered in this work can be viewed as an example of solutions that can empower us with great flexibility in the systematic analysis and explanation of complex phenomena that arise in a variety of problems, including protein chemistry, fluid mechanics, plasma physics, optical fibers, and shallow water wave propagation.

Lump, multi-lump, cross kinky-lump and manifold periodic-soliton solutions for the (2+1)-D Calogero-Bogoyavlenskii-Schiff equation

A bilinear form of the (2+1)-dimensional nonlinear Calogero-Bogoyavlenskii-Schiff (CBS) model is derived using a transformation of dependent variable, which contain a controlling parameter. This parameter can control the direction, wave height and angle of the traveling wave. Based on the Hirota bilinear form and ansatz functions, we build many types of novel structures and manifold periodic-soliton solutions to the CBS model. In particular, we obtain entirely exciting periodic-soliton, cross-kinky-lump wave, double kinky-lump wave, periodic cross-kinky-lump wave, periodic two-solitary wave solutions as well as breather style of two-solitary wave solutions. We present their propagation features via changing the existence parametric values in graphically. In addition, we estimate a condition that the waves are propagated obliquely for η ≠ 0 , and orthogonally for η = 0 .