scholarly journals Travelling Wave Solutions of Nonlinear Dynamical Equations in a Double-Chain Model of DNA

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Zheng-yong Ouyang ◽  
Shan Zheng
Keyword(s):  
Solitary Waves ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Travelling Wave ◽  
Elastic Membrane ◽  
Chain Model ◽  
Double Chain ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Wave Solutions

We consider the nonlinear dynamics in a double-chain model of DNA which consists of two long elastic homogeneous strands connected with each other by an elastic membrane. By using the method of dynamical systems, the bounded traveling wave solutions such as bell-shaped solitary waves and periodic waves for the coupled nonlinear dynamical equations of DNA model are obtained and simulated numerically. For the same wave speed, bell-shaped solitary waves of different heights are found to coexist.

scholarly journals Minimal Wave Speed in a Predator-Prey System with Distributed Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Time Delay ◽  
Traveling Wave ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Predator Prey ◽  
Wave Solutions ◽  
Prey System ◽  
Minimal Wave Speed ◽  
Distributed Time Delay

This paper is concerned with the minimal wave speed of traveling wave solutions in a predator-prey system with distributed time delay, which does not satisfy comparison principle due to delayed intraspecific terms. By constructing upper and lower solutions, we obtain the existence of traveling wave solutions when the wave speed is the minimal wave speed. Our results complete the known conclusions and show the precisely asymptotic behavior of traveling wave solutions.

Minimal wave speed of a diffusive SIR epidemic model with nonlocal delay

2019 ◽  
Vol 12 (07) ◽  
pp. 1950081
Author(s):  
Fuzhen Wu ◽  
Dongfeng Li
Keyword(s):  
Traveling Wave ◽  
Epidemic Model ◽  
Wave Speed ◽  
Traveling Wave Solutions ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Nonlocal Delay ◽  
Spatial Nonlocality ◽  
Wave Solutions ◽  
Minimal Wave Speed

This paper is concerned with the minimal wave speed in a diffusive epidemic model with nonlocal delays. We define a threshold. By presenting the existence and the nonexistence of traveling wave solutions for all positive wave speed, we confirm that the threshold is the minimal wave speed of traveling wave solutions, which models that the infective invades the habitat of the susceptible. For some cases, it is proven that spatial nonlocality may increase the propagation threshold while time delay decreases the threshold.

DIVERSITY OF TRAVELING WAVE SOLUTIONS IN DELAYED CELLULAR NEURAL NETWORKS

2008 ◽  
Vol 18 (12) ◽  
pp. 3515-3550 ◽  
Author(s):  
CHENG-HSIUNG HSU ◽  
CHUN-HSIEN LI ◽  
SUH-YUH YANG
Keyword(s):  
Neural Networks ◽  
Traveling Wave ◽  
Wave Speed ◽  
Distributed Delay ◽  
Traveling Wave Solutions ◽  
Cellular Neural Networks ◽  
Monotonicity Condition ◽  
Switching Speed ◽  
Wave Solutions ◽  
Special Cases

This work investigates the diversity of traveling wave solutions for a class of delayed cellular neural networks on the one-dimensional integer lattice ℤ1. The dynamics of a given cell is characterized by instantaneous self-feedback and neighborhood interaction with distributed delay due to, for example, finite switching speed and finite velocity of signal transmission. Applying the monotone iteration scheme, we can deduce the existence of monotonic traveling wave solutions provided the templates satisfy the so-called quasi-monotonicity condition. We then consider two special cases of the delayed cellular neural network in which each cell interacts only with either the nearest m left neighbors or the nearest m right neighbors. For the former case, we can directly figure out the analytic solution in an explicit form by the method of step with the help of the characteristic function and then prove that, in addition to the existence of monotonic traveling wave solutions, for certain templates there exist nonmonotonic traveling wave solutions such as camel-like waves with many critical points. For the latter case, employing the comparison arguments repeatedly, we can clarify the deformation of traveling wave solutions with respect to the wave speed. More specifically, we can describe the transition of profiles from monotonicity, damped oscillation, periodicity, unboundedness and back to monotonicity as the wave speed is varied. Some numerical results are also given to demonstrate the theoretical analysis.

scholarly journals Asymmetric gravity–capillary solitary waves on deep water

2014 ◽  
Vol 759 ◽  
Author(s):  
Z. Wang ◽  
J.-M. Vanden-Broeck ◽  
P. A. Milewski
Keyword(s):  
Wave Propagation ◽  
Solitary Waves ◽  
Travelling Wave ◽  
Propagation Direction ◽  
Travelling Wave Solutions ◽  
Two Dimensional ◽  
Bifurcation Curve ◽  
Wave Propagation Direction ◽  
Wave Solutions ◽  
Deep Fluid

AbstractWe present new families of gravity–capillary solitary waves propagating on the surface of a two-dimensional deep fluid. These spatially localised travelling-wave solutions are non-symmetric in the wave propagation direction. Our computation reveals that these waves appear from a spontaneous symmetry-breaking bifurcation, and connect two branches of multi-packet symmetric solitary waves. The speed–energy bifurcation curve of asymmetric solitary waves features a zigzag behaviour with one or more turning points.

Stability analysis and applications of traveling wave solutions of three-dimensional nonlinear modified Zakharov–Kuznetsov equation in a magnetized plasma

2018 ◽  
Vol 33 (25) ◽  
pp. 1850145 ◽  
Author(s):  
Abdullah ◽  
Aly R. Seadawy ◽  
Jun Wang
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Electrostatic Field ◽  
Three Dimensional ◽  
Field Potential ◽  
Traveling Wave Solutions ◽  
Mapping Method ◽  
Magnetized Plasma ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Propagation of three-dimensional nonlinear solitary waves in a magnetized electron–positron plasma is analyzed. Modified extended mapping method is further modified and applied to three-dimensional nonlinear modified Zakharov–Kuznetsov equation to find traveling solitary wave solutions. As a result, electrostatic field potential, electric field, magnetic field and quantum statistical pressure are obtained with the aid of Mathematica. The new exact solitary wave solutions are obtained in different forms such as periodic, kink and anti-kink, dark soliton, bright soliton, bright and dark solitary waves, etc. The results are expressed in the forms of trigonometric, hyperbolic, rational and exponential functions. The electrostatic field potential and electric and magnetic fields are shown graphically. The soliton stability of these solitary wave solutions is analyzed. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical physical problems.

scholarly journals Travelling wave solutions for a surface wave equation in fluid mechanics

2016 ◽  
Vol 20 (3) ◽  
pp. 893-898 ◽  
Author(s):  
Yi Tian ◽  
Zai-Zai Yan
Keyword(s):  
Wave Equation ◽  
Fluid Mechanics ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Linear Wave ◽  
Travelling Wave Solutions ◽  
Linear Wave Equation ◽  
Wave Solutions

This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

scholarly journals DISPERSIVE SOLITARY WAVE SOLUTIONS OF COUPLING BOITI-LEON-PEMPINELLI SYSTEM USING TWO DIFFERENT METHODS

2021 ◽  
Vol 21 (1) ◽  
pp. 91-104
Author(s):  
MAHA S.M. SHEHATA ◽  
HADI REZAZADEH ◽  
EMAD H.M. ZAHRAN ◽  
MOSTAFA ESLAMI ◽  
AHMET BEKIR
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
The Other ◽  
Solitary Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Special Value ◽  
Ode Method

In this paper, new exact traveling wave solutions for the coupling Boiti-Leon-Pempinelli system are obtained by using two important different methods. The first is the modified extended tanh function methods which depend on the balance rule and the second is the Ricatti-Bernoulli Sub-ODE method which doesn’t depend on the balance rule. The solitary waves solutions can be derived from the exact wave solutions by give the parameters a special value. The consistent and inconsistent of the obtained solutions are studied not only between these two methods but also with that relisted by the other methods.

scholarly journals Computational and traveling wave analysis of Tzitzéica and Dodd-Bullough-Mikhailov equations: An exact and analytical study

2021 ◽  
Vol 10 (1) ◽  
pp. 272-281
Author(s):  
Hülya Durur ◽  
Asıf Yokuş ◽  
Kashif Ali Abro
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Stationary Wave ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Wave Solutions

Abstract Computational and travelling wave solutions provide significant improvements in accuracy and characterize novelty of imposed techniques. In this context, computational and travelling wave solutions have been traced out for Tzitzéica and Dodd-Bullough-Mikhailov equations by means of (1/G′)-expansion method. The different types of solutions have constructed for Tzitzéica and Dodd-Bullough-Mikhailov equations in hyperbolic form. Moreover, solution function of Tzitzéica and Dodd-Bullough-Mikhailov equations has been derived in the format of logarithmic nature. Since both equations contain exponential terms so the solutions produced are expected to be in logarithmic form. Traveling wave solutions are presented in different formats from the solutions introduced in the literature. The reliability, effectiveness and applicability of the (1/G′)-expansion method produced hyperbolic type solutions. For the sake of physical significance, contour graphs, two dimensional and three dimensional graphs have been depicted for stationary wave. Such graphical illustration has been contrasted for stationary wave verses traveling wave solutions. Our graphical comparative analysis suggests that imposed method is reliable and powerful method for obtaining exact solutions of nonlinear evolution equations.

scholarly journals Propagation of stochastic travelling waves of cooperative systems with noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hao Wen ◽  
Jianhua Huang ◽  
Yuhong Li
Keyword(s):  
Dynamical System ◽  
White Noise ◽  
Wave Speed ◽  
Travelling Waves ◽  
Equilibrium Points ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Cooperative System ◽  
Wave Solutions ◽  
Suitable Marker

<p style='text-indent:20px;'>We consider the cooperative system driven by a multiplicative It\^o type white noise. The existence and their approximations of the travelling wave solutions are proven. With a moderately strong noise, the travelling wave solutions are constricted by choosing a suitable marker of wavefront. Moreover, the stochastic Feynman-Kac formula, sup-solution, sub-solution and equilibrium points of the dynamical system corresponding to the stochastic cooperative system are utilized to estimate the asymptotic wave speed, which is closely related to the white noise.</p>

scholarly journals Nonlinear dynamical properties of solitary wave solutions for Zakharov-Kuznetsov equation in a multicomponent plasma

2021 ◽  
Vol 67 (6 Nov-Dec) ◽  
Author(s):  
U.M. Abdelsalam
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Traveling Wave Solutions ◽  
Reductive Perturbation Method ◽  
Physical Parameters ◽  
Nonlinear Dynamical ◽  
Multicomponent Plasma ◽  
Wave Solutions ◽  
Laboratory Plasmas ◽  
Component Plasma

Using the reductive perturbation method, we have derived the Zakharov-Kuznetsov (ZK) equation for a multi-component plasma model consisting of electrons, positrons and the uid ions with positive and negative charges. The extended homogenous balance method has been applied to obtain the soliton solution in addition to many traveling wave solutions. various physical parameters have different effects on the profile of the solitary wave pulses which can show the propagation of the ion acoustic waves in laboratory plasmas and many astrophysical plasma systems as in Earth's ionosphere.

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