scholarly journals Ion-Acoustic Solitary Wave Solutions of Three-Dimensional Zakharov-KuznetsovBurgers Equation for Dust Ion Acoustic Waves and Their Applications

2019 ◽  
Vol 2 (1) ◽  
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Field Potential ◽  
Traveling Wave Solutions ◽  
Physical Models ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ion Acoustic

Modified extended mapping method is further modified to discover traveling wave solutions of non- linear complex physical models, arising in various fields of applied sciences. The method is applied to three-dimensional ZakharovKuznetsov-Burgers equation in magnetized dusty plasma. Consequently different kinds of families of exact traveling wave solutions that represent electric field potential, electric and magnetic fields are fruitfully surveyed, with the help of Mathematica. The obtained novel exact traveling wave solutions are in different forms such as bright and dark solitary wave, periodic solitary wave, dark and bright soliton, etc., that are represented in the forms of trigonometric, hyperbolic, exponential and rational functions. The properties of some of the novel traveling wave solutions are shown by figures. The obtained results exhibit the effectiveness, power and exactness of the method that can be used for many other nonlinear problems.

Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

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 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 Different Kinds of Singular and Nonsingular Exact Traveling Wave Solutions of the Kudryashov-Sinelshchikov Equation in the Special Parametric Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Can Chen ◽  
Weiguo Rui ◽  
Yao Long
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Dynamic Behaviors ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

In this paper, by using the integral bifurcation method, we studied the Kudryashov-Sinelshchikov equation. In the special parametric conditions, some singular and nonsingular exact traveling wave solutions, such as periodic cusp-wave solutions, periodic loop-wave solutions, smooth loop-soliton solutions, smooth solitary wave solutions, periodic double wave solutions, periodic compacton solutions, and nonsmooth peakon solutions are obtained. Further more, the dynamic behaviors of these exact traveling wave solutions are investigated. It is found that the waveforms of some traveling wave solutions vary with the changes of parameters.

Bifurcation and Traveling Wave Solutions for the Fokas Equation

2015 ◽  
Vol 25 (10) ◽  
pp. 1550136 ◽  
Author(s):  
Jibin Li ◽  
Zhijun Qiao
Keyword(s):  
Phase Space ◽  
Solitary Wave ◽  
Traveling Wave ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Phase Space Analysis ◽  
Space Analysis ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

This paper is devoted to discussing bifurcation and traveling wave solutions for the Fokas equation. By investigating the dynamical behavior with phase space analysis, we may derive all possible exact traveling wave solutions, including compactons, cuspons, periodic cusp wave solutions, and smooth solitary wave solutions.

scholarly journals Exact Traveling Wave Solutions for a Nonlinear Evolution Equation of Generalized Tzitzéica-Dodd-Bullough-Mikhailov Type

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Weiguo Rui
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Blow Up ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave

By using the integral bifurcation method, a generalized Tzitzéica-Dodd-Bullough-Mikhailov (TDBM) equation is studied. Under different parameters, we investigated different kinds of exact traveling wave solutions of this generalized TDBM equation. Many singular traveling wave solutions with blow-up form and broken form, such as periodic blow-up wave solutions, solitary wave solutions of blow-up form, broken solitary wave solutions, broken kink wave solutions, and some unboundary wave solutions, are obtained. In order to visually show dynamical behaviors of these exact solutions, we plot graphs of profiles for some exact solutions and discuss their dynamical properties.

EXACT TRAVELING WAVE SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS WITH NONLINEAR TERMS OF ANY ORDER

2003 ◽  
Vol 14 (01) ◽  
pp. 99-112 ◽  
Author(s):  
YONG CHEN ◽  
BIAO LI ◽  
HONG-QING ZHANG
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Rational Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

In this paper, we improved the tanh method by means of a proper transformation and general ansätz. Using the improved method, with the aid of Mathematica™, we consider some nonlinear evolution equations with nonlinear terms of any order. As a result, rich explicit exact traveling wave solutions for these equations, which contain kink profile solitary wave solutions, bell profile solitary wave solutions, rational solutions, periodic solutions, and combined formal solutions, are obtained.

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