Unified Method Applied to the New Hamiltonian Amplitude Equation: Wave Solutions and Stability Analysis

2021 ◽  
Author(s):  
Islam S M Rayhanul ◽  
Dipankar Kumar ◽  
Akbar M Ali
Keyword(s):  
Stability Analysis ◽  
Amplitude Equation ◽  
Wave Solutions ◽  
Unified Method

scholarly journals The new exact solitary wave solutions and stability analysis for the ( 2 + 1 ) $(2+1)$ -dimensional Zakharov–Kuznetsov equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Behzad Ghanbari ◽  
Abdullahi Yusuf ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Propagation of frontal polymerization—crystallization waves

1994 ◽  
Vol 5 (2) ◽  
pp. 201-215 ◽  
Author(s):  
Vit. Volpert ◽  
Vl. Volpert
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Linear Stability Analysis ◽  
Hot Spot ◽  
Travelling Wave ◽  
Frontal Polymerization ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Planar Front ◽  
Cylindrical Reactor

We consider polymerization–crystallization waves in a cylindrical reactor, in which monomer is converted to polymer in a planar front. The polymer is subsequently crystallized in a wider zone behind the front. Specifically, we study uniformly propagating polymerization–crystallization waves, and determine profiles of temperature, and concentrations of polymer and crystallized polymer, as well as the propagation velocity. A linear stability analysis of the travelling wave solutions indicates the possibility of Hopf bifurcation, which describes the transition to the experimentally observed spinning mode of propagation, in which a hot spot is observed to propagate along a helical path on the surface of the cylinder. Since conditions at the time of conversion determine the nature of the polymer produced, spiral hollows, which trace out a helical path, appear on the surface of the crystallized polymer product.

Periodic wave solutions and stability analysis for the (3+1)-D potential-YTSF equation arising in fluid mechanics

2020 ◽  
pp. 1-23
Author(s):  
Jalil Manafian ◽  
Onur Alp Ilhan ◽  
Hajar Farhan Ismael ◽  
Sizar Abid Mohammed ◽  
Saadat Mazanova
Keyword(s):  
Stability Analysis ◽  
Fluid Mechanics ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Ytsf Equation ◽  
Potential Ytsf Equation

Exact Periodic Wave Solutions to a New Hamiltonian Amplitude Equation

2003 ◽  
Vol 72 (6) ◽  
pp. 1356-1359 ◽  
Author(s):  
Yan-ze Peng
Keyword(s):  
Periodic Wave ◽  
Amplitude Equation ◽  
Periodic Wave Solutions ◽  
Wave Solutions

Stability analysis of plane wave solutions of the discrete Ginzburg-Landau equation

2000 ◽  
Vol 61 (1) ◽  
pp. 390-393 ◽  
Author(s):  
J. F. Ravoux ◽  
S. Le Dizès ◽  
P. Le Gal
Keyword(s):  
Stability Analysis ◽  
Plane Wave ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Wave Solutions ◽  
Ginzburg Landau Equation

scholarly journals Traveling wave solutions for (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity

2019 ◽  
Vol 8 (1) ◽  
pp. 559-567 ◽  
Author(s):  
M.S. Osman ◽  
Hadi Rezazadeh ◽  
Mostafa Eslami
Keyword(s):  
Applied Sciences ◽  
Power Law ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Mathematical Tool ◽  
Rational Solutions ◽  
Wave Solutions ◽  
The Unified Method ◽  
Soliton Wave Solutions ◽  
Unified Method

Abstract In this work, we consider the (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Solitary wave solutions, soliton wave solutions, elliptic wave solutions, and periodic (hyperbolic) wave rational solutions are obtained by means of the unified method. The solutions showed that this method provides us with a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various fields of applied sciences.

scholarly journals Stability Analysis and Assortment of Exact Traveling Wave Solutions for the (2+1)-Dimensional Boiti-Leon-Pempinelli System

2021 ◽  
pp. 2393-2400
Author(s):  
Mizal H. Alobaidi ◽  
Wafaa M. Taha ◽  
Ali H. Hazza ◽  
Pelumi E. Oguntunde
Keyword(s):  
Stability Analysis ◽  
Traveling Wave ◽  
Physical Meaning ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Exact Results ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
The Stability

     In this research, the Boiti–Leon–Pempinelli (BLP) system was used to understand the physical meaning of exact and solitary traveling wave solutions. To establish modern exact results, considered. In addition, the results obtained were compared with those obtained by using other existing methods, such as the standard hyperbolic tanh function method, and the stability analysis for the results was discussed.

Modulational instability in a biexciton molecular chain with saturable nonlinearity effects

2016 ◽  
Vol 30 (01) ◽  
pp. 1550244
Author(s):  
Issa Sali ◽  
C. B. Tabi ◽  
H. P. Ekobena ◽  
T. C. Kofané
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability Analysis ◽  
Adiabatic Approximation ◽  
Continuous Wave ◽  
Modulational Instability ◽  
Coupled System ◽  
Molecular Chain ◽  
Saturable Nonlinearity ◽  
Wave Solutions

In this paper, we study the modulational instability (MI) in a biexciton molecular chain taking into account the saturable nonlinearity effects (SNE). Under the adiabatic approximation, the biexciton system is reduced to two coupled nonlinear Schrödinger equations. We perform the linear stability analysis of continuous wave solutions of the coupled system. This analysis reveals that the MI gain is deeply influenced by the SNE. Indeed, the gain spectrum decreases when increasing the saturable nonlinearity parameters. The numerical simulations reveal that the system exhibits incoherent periodic array of patterns and we also observe train of pulses due to the SNE.

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