scholarly journals Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity

2019 ◽  
Vol 13 (1) ◽  
pp. 1060-1072 ◽  
Author(s):  
Aly R. Seadawy ◽  
Mujahid Iqbal ◽  
Dianchen Lu
Keyword(s):  
Heat Transfer ◽  
Nonlinear Wave ◽  
Dynamical Equation ◽  
Gas Bubbles ◽  
Wave Solutions ◽  
Nonlinear Wave Solutions

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.

Quantum corrections to nonlinear wave solutions

1976 ◽  
Vol 13 (8) ◽  
pp. 2278-2286 ◽  
Author(s):  
Laurence Jacobs
Keyword(s):  
Nonlinear Wave ◽  
Quantum Corrections ◽  
Wave Solutions ◽  
Nonlinear Wave Solutions

scholarly journals The explicit nonlinear wave solutions of the generalized $b$-equation

2012 ◽  
Vol 12 (2) ◽  
pp. 1029-1047
Author(s):  
Liu Rui
Keyword(s):  
Nonlinear Wave ◽  
Wave Solutions ◽  
Nonlinear Wave Solutions

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

Abundant soliton wave solutions for the (3+1)-dimensional variable-coefficient nonlinear wave equation in liquid with gas bubbles by bilinear analysis

2021 ◽  
Author(s):  
Guanqi Tao ◽  
Jalil Manafian ◽  
Onur Alp İlhan ◽  
Syed Maqsood Zia ◽  
Latifa Agamalieva
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Variable Coefficient ◽  
Soliton Solutions ◽  
Gas Bubbles ◽  
Soliton Theory ◽  
Wave Solutions ◽  
Dimensional Variable ◽  
Hirota Bilinear

In this paper, we check and scan the (3+1)-dimensional variable-coefficient nonlinear wave equation which is considered in soliton theory and generated by considering the Hirota bilinear operators. We retrieve some novel exact analytical solutions, including cross-kink soliton solutions, breather wave solutions, interaction between stripe and periodic, multi-wave solutions, periodic wave solutions and solitary wave solutions for the (3+1)-dimensional variable-coefficient nonlinear wave equation in liquid with gas bubbles by Maple symbolic computations. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota bilinear forms and their generalized equivalences. Lastly, the graphical simulations of the exact solutions are depicted.

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.

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