New Solitary-Wave Solutions for the Generalized Reaction Duffing Model and their Dynamics

2004 ◽  
Vol 59 (11) ◽  
pp. 721-728 ◽  
Author(s):  
Jong-Jae Kim ◽  
Woo-Pyo Hong
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Driving Force ◽  
Function Method ◽  
Auxiliary Function ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Dynamical Properties ◽  
Duffing Model ◽  
52.35 Mw

We find new analytic solitary-wave solutions, having a nonzero background at infinity, of the generalized reaction Duffing model using the auxiliary function method. We study the dynamical properties of the solitary-waves by numerical simulations. It is shown that the solitary-waves can be stable or unstable depending on the coefficients of the model. We study the interaction dynamics by using the solitary-waves as initial profiles to show that the nonlinear terms may act as an effective driving force. - PACS numbers: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

On Solitary-Wave Solutions for the Coupled Korteweg – de Vries and Modified Korteweg – de Vries Equations and their Dynamics

2006 ◽  
Vol 61 (3-4) ◽  
pp. 125-132 ◽  
Author(s):  
Woo-Pyo Hong
Keyword(s):  
Solitary Wave ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Function Method ◽  
Auxiliary Function ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries ◽  
Dynamical Properties ◽  
52.35 Mw

Analytic sech4-type traveling solitary-wave solutions of the coupled Korteweg-de Vries and modified Korteweg-de Vries equations proposed by Kersten-Krasil’shchik, are found by applying the auxiliary function method. The dynamical properties of the solitary-waves are studied by numerical simulations. - PACS numbers: 03.40.Kf, 02.30.Jr, 47.20.Ky, 52.35.Mw

scholarly journals Existence and linearized stability of solitary waves for a quasilinear Benney system

2016 ◽  
Vol 146 (3) ◽  
pp. 547-564 ◽  
Author(s):  
João-Paulo Dias ◽  
Mário Figueira ◽  
Filipe Oliveira
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Compact Support ◽  
Travelling Waves ◽  
Standing Waves ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Linearized Stability ◽  
Stability Of Solitary Waves ◽  
Image Position

We prove the existence of solitary wave solutions to the quasilinear Benney systemwhere , –1 < p < +∞ and a, γ > 0. We establish, in particular, the existence of travelling waves with speed arbitrarily large if p < 0 and arbitrarily close to 0 if . We also show the existence of standing waves in the case , with compact support if – 1 < p < 0. Finally, we obtain, under certain conditions, the linearized stability of such solutions.

Solitary wave solutions of (2+1)-dimensional Maccari system

2021 ◽  
pp. 2150391
Author(s):  
Ghazala Akram ◽  
Naila Sajid
Keyword(s):  
Nonlinear Optics ◽  
Solitary Wave ◽  
Plasma Physics ◽  
Exact Solutions ◽  
Function Method ◽  
Expansion Method ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Solitary Wave Solutions ◽  
Wave Solutions

In this article, three mathematical techniques have been operationalized to discover novel solitary wave solutions of (2+1)-dimensional Maccari system, which also known as soliton equation. This model equation is usually of applicative relevance in hydrodynamics, nonlinear optics and plasma physics. The [Formula: see text] function, the hyperbolic function and the [Formula: see text]-expansion techniques are used to obtain the novel exact solutions of the (2+1)-dimensional Maccari system (arising in nonlinear optics and in plasma physics). Many novel solutions such as periodic wave solutions by [Formula: see text] function method, singular, combined-singular and periodic solutions by hyperbolic function method, hyperbolic, rational and trigonometric solutions by [Formula: see text]-expansion method are obtained. The exact solutions are shown through 3D graphics which present the movement of the obtained solutions.

Analyticity of solitary wave solutions to generalized Kadomtsev—Petviashvili equations

2001 ◽  
Vol 131 (2) ◽  
pp. 391-424 ◽  
Author(s):  
Keiichi Kato ◽  
Patrick-Nicolas Pipolo
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Linear And Nonlinear

In this paper we prove the existence and analyticity of solitary waves of generalized Kadomtsev–Petviashvili equations satisfying a set of conditions on linear and nonlinear terms which determine their behaviour at infinity and around 0.

The Multiple Exp-Function Method and the Linear Superposition Principle for Solving the (2+1)-Dimensional Calogero–Bogoyavlenskii–Schiff Equation

2015 ◽  
Vol 70 (9) ◽  
pp. 775-779 ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Function Method ◽  
Superposition Principle ◽  
Solitary Wave Solutions ◽  
Linear Superposition ◽  
Wave Solutions ◽  
Linear Superposition Principle

AbstractIn this article, the multiple exp-function method and the linear superposition principle are employed for constructing the exact solutions and the solitary wave solutions for the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. With help of Maple and by using the multiple exp-method, we can get exact explicit one-wave, two-wave, and three-wave solutions, which include one-soliton-, two-soliton-, and three-soliton-type solutions. Furthermore, we apply the linear superposition principle to find n-wave solutions of the CBS equation. Two cases with specific values of the involved parameters are plotted for each two-wave and three-wave solutions.

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 Gaussian solitary waves to Boussinesq equation with dual dispersion and logarithmic nonlinearity

2018 ◽  
Vol 23 (6) ◽  
pp. 942-950 ◽  
Author(s):  
Anjan Biswasa ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Trial Function ◽  
Boussinesq Equation ◽  
Solitary Wave Solutions ◽  
Shallow Water Waves ◽  
Wave Solutions ◽  
Extended Trial

This paper discusses shallow water waves that is modeled with Boussinesq equation that comes with dual dispersion and logarithmic nonlinearity. The extended trial function scheme retrieves exact Gaussian solitary wave solutions to the model.

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.

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