scholarly journals (2+1)-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Chunlei Wang ◽  
Yong Zhang ◽  
Baoshu Yin ◽  
Xiaoen Zhang
Keyword(s):  
Solitary Wave ◽  
Riccati Equation ◽  
Lie Algebra ◽  
Integrable System ◽  
Solitary Waves ◽  
Mkdv Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Rossby Solitary Waves ◽  
Mkdv Hierarchy

By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new (2+1)-dimensional mKdV hierarchy is derived which popularizes the results of (1+1)-dimensional integrable system. Furthermore, the (2+1)-dimensional mKdV equation can be applied to describe the propagation of the Rossby solitary waves in the plane of ocean and atmosphere, which is different from the (1+1)-dimensional mKdV equation. By virtue of Riccati equation, some solutions of (2+1)-dimensional mKdV equation are obtained. With the help of solitary wave solutions, similar to the fiber soliton communication, the chirp effect of Rossby solitary waves is discussed and some conclusions are given.

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.

A New Type of Solitary Wave Solution of the mKdV Equation Under Singular Perturbations

2020 ◽  
Vol 30 (11) ◽  
pp. 2050162
Author(s):  
Lijun Zhang ◽  
Maoan Han ◽  
Mingji Zhang ◽  
Chaudry Masood Khalique
Keyword(s):  
Solitary Wave ◽  
Singular Perturbations ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Mkdv Equation ◽  
Geometric Singular Perturbation Theory ◽  
Solitary Wave Solutions ◽  
Wave Speeds ◽  
Wave Solutions ◽  
New Type

In this work, we examine the solitary wave solutions of the mKdV equation with small singular perturbations. Our analysis is a combination of geometric singular perturbation theory and Melnikov’s method. Our result shows that two families of solitary wave solutions of mKdV equation, having arbitrary positive wave speeds and infinite boundary limits, persist for selected wave speeds after small singular perturbations. More importantly, a new type of solitary wave solution possessing both valley and peak, named as breather in physics, which corresponds to a big homoclinic loop of the associated dynamical system is observed. It reveals an exotic phenomenon and exhibits rich dynamics of the perturbed nonlinear wave equation. Numerical simulations are performed to further detect the wave speeds of the persistent solitary waves and the nontrivial one with both valley and peak.

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.

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.

scholarly journals On the breather waves, rogue waves and solitary waves to a generalized (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4959-4969 ◽  
Author(s):  
Wei-Qi Peng ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Bilinear Form ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Solitary Wave Solutions ◽  
Bell Polynomial ◽  
Wave Solutions ◽  
Extreme Behavior ◽  
Natural Way

In this paper, we consider a generalized (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera- Sawada (CDGKS) equation. By using the Bell polynomial, we derive its bilinear form. Based on the homoclinic breather limit method, we construct the homoclinic breather wave and the rational rogue wave solutions of the equation. Then by using its bilinear form, some solitary wave solutions of the CDGKS equation are provided by a very natural way. Moreover, some prominent characteristics for the dynamic behaviors of these solitons are analyzed by several graphics. Our results show that the breather wave can be transformed into rogue wave under the extreme behavior.

Sign in / Sign up

Export Citation Format

Share Document