Some Nonlinear Wave Solutions for the Generalized Fornberg-Whitham Equation

2020 ◽  
Vol 09 (09) ◽  
pp. 1589-1603
Author(s):  
贇 朱
Keyword(s):  
Nonlinear Wave ◽  
Wave Solutions ◽  
Nonlinear Wave Solutions ◽  
Whitham Equation

scholarly journals Nonlinear Wave Solutions of Cylindrical KdV-Burgers Equation in Nonextensive Plasmas for Astrophysical Objects

2020 ◽  
Vol 137 (6) ◽  
pp. 1061-1067
Author(s):  
U.M. Abdelsalam ◽  
M.S. Zobaer ◽  
H. Akther ◽  
M.G.M. Ghazal ◽  
M.M. Fares
Keyword(s):  
Nonlinear Wave ◽  
Burgers Equation ◽  
Wave Solutions ◽  
Astrophysical Objects ◽  
Nonlinear Wave Solutions

scholarly journals Control of Nonlinear Wave Solutions to Neural Field Equations

2019 ◽  
Vol 18 (2) ◽  
pp. 1015-1036 ◽  
Author(s):  
Alexander Ziepke ◽  
Steffen Martens ◽  
Harald Engel
Keyword(s):  
Nonlinear Wave ◽  
Neural Field ◽  
Field Equations ◽  
Wave Solutions ◽  
Neural Field Equations ◽  
Nonlinear Wave Solutions

COEXISTENCE OF MULTIFARIOUS EXACT NONLINEAR WAVE SOLUTIONS FOR GENERALIZED b-EQUATION

2010 ◽  
Vol 20 (10) ◽  
pp. 3193-3208 ◽  
Author(s):  
RUI LIU
Keyword(s):  
Nonlinear Wave ◽  
Wave Solution ◽  
Wave Speed ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Periodic Wave Solution ◽  
Wave Solutions ◽  
Special Cases ◽  
Singular Wave ◽  
Nonlinear Wave Solutions

In this paper, we consider the generalized b-equation ut - uxxt + (b + 1)u2ux = buxuxx + uxxx. For a given constant wave speed, we investigate the coexistence of multifarious exact nonlinear wave solutions including smooth solitary wave solution, peakon wave solution, smooth periodic wave solution, single singular wave solution and periodic singular wave solution. Not only is the coexistence shown, but the concrete expressions are given via phase analysis and special integrals. From our work, it can be seen that the types of exact nonlinear wave solutions of the generalized b-equation are more than that of the b-equation. Many previous results are turned to our special cases. Also, some conjectures and questions are presented.

scholarly journals Exact explicit nonlinear wave solutions to a modified cKdV equation

2020 ◽  
Vol 5 (5) ◽  
pp. 4917-4930
Author(s):  
Zhenshu Wen ◽  
◽  
Lijuan Shi
Keyword(s):  
Nonlinear Wave ◽  
Wave Solutions ◽  
Nonlinear Wave Solutions

THE EXPLICIT NONLINEAR WAVE SOLUTIONS AND THEIR BIFURCATIONS OF THE GENERALIZED CAMASSA–HOLM EQUATION

2011 ◽  
Vol 21 (11) ◽  
pp. 3119-3136 ◽  
Author(s):  
ZHENGRONG LIU ◽  
YONG LIANG
Keyword(s):  
Solitary Wave ◽  
Nonlinear Wave ◽  
Wave Solution ◽  
Wave Speed ◽  
Solitary Wave Solution ◽  
Wave Solutions ◽  
Holm Equation ◽  
Bifurcation Phenomena ◽  
Singular Wave ◽  
Nonlinear Wave Solutions

In this paper, we study the explicit nonlinear wave solutions and their bifurcations of the generalized Camassa–Holm equation [Formula: see text]Not only are the precise expressions of the explicit nonlinear wave solutions obtained, but some interesting bifurcation phenomena are revealed.Firstly, it is verified that k = 3/8 is a bifurcation parametric value for several types of explicit nonlinear wave solutions.When k < 3/8, there are five types of explicit nonlinear wave solutions, which are(i) hyperbolic peakon wave solution,(ii) fractional peakon wave solution,(iii) fractional singular wave solution,(iv) hyperbolic singular wave solution,(v) hyperbolic smooth solitary wave solution.When k = 3/8, there are two types of explicit nonlinear wave solutions, which are fractional peakon wave solution and fractional singular wave solution.When k > 3/8, there is not any type of explicit nonlinear wave solutions.Secondly, it is shown that there are some bifurcation wave speed values such that the peakon wave and the anti-peakon wave appear alternately.Thirdly, it is displayed that there are other bifurcation wave speed values such that the hyperbolic peakon wave solution becomes the fractional peakon wave solution, and the hyperbolic singular wave solution becomes the fractional singular wave solution.

Dynamical behavior of nonlinear wave solutions of the generalized Newell–Whitehead–Segel equation

2020 ◽  
Vol 31 (04) ◽  
pp. 2050059
Author(s):  
Asit Saha ◽  
Amiya Das
Keyword(s):  
Nonlinear Wave ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Phase Portraits ◽  
Phase Plane Analysis ◽  
Linear Coefficient ◽  
Wave Solutions ◽  
Nonlinear Wave Solutions

Dynamical behavior of nonlinear wave solutions of the perturbed and unperturbed generalized Newell–Whitehead–Segel (GNWS) equation is studied via analytical and computational approaches for the first time in the literature. Bifurcation of phase portraits of the unperturbed GNWS equation is dispensed using phase plane analysis through symbolic computation and it shows stable oscillation of the traveling waves. Chaotic behavior of the perturbed GNWS equation is obtained by applying different computational tools, like phase plot, time series plot, Poincare section, bifurcation diagram and Lyapunov exponent. A period-doubling bifurcation behavior to chaotic behavior is shown for the perturbed GNWS equation and again it shows chaotic to periodic motion through inverse period-doubling bifurcation. The perturbed GNWS equation also shows chaotic motion through a sequence of periodic motions (period-1, period-3 and period-5) depending on the variation of the parameter of linear coefficient. Thus, the parameter of linear coefficient plays the role of a controlling parameter in the chaotic dynamics of the perturbed GNWS equation.

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