Quasilinear Fourth-Order Hyperbolic Boussinesq Equation: Shock, Rarefaction, and Fundamental Solutions

2014 ◽  
pp. 297-316
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Fundamental Solutions

scholarly journals Regarding New Wave Patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 341 ◽  
Author(s):  
Juan Luis García Guirao ◽  
Haci Mehmet Baskonus ◽  
Ajay Kumar
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Bright Soliton ◽  
New Wave ◽  
Wave Patterns

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.

scholarly journals A Fourth Order Finite Difference Method for the Good Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
M. S. Ismail ◽  
Farida Mosally
Keyword(s):  
Exact Solution ◽  
Nonlinear System ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
First Order ◽  
System A ◽  
Accuracy And Stability ◽  
Linearization Techniques

The “good” Boussinesq equation is transformed into a first order differential system. A fourth order finite difference scheme is derived for this system. The resulting scheme is analyzed for accuracy and stability. Newton’s method and linearization techniques are used to solve the resulting nonlinear system. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the derived method. Head-on and overtaking interactions of two solitons are also considered. The numerical results reveal the good performance of the derived method.

High Order Energy-Preserving Method of the “Good” Boussinesq Equation

2016 ◽  
Vol 9 (1) ◽  
pp. 111-122 ◽  
Author(s):  
Chaolong Jiang ◽  
Jianqiang Sun ◽  
Xunfeng He ◽  
Lanlan Zhou
Keyword(s):  
Vector Field ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
Field Method ◽  
High Order ◽  
Discrete Energy ◽  
High Order Scheme ◽  
Order Energy ◽  
Order Scheme ◽  
Pseudo Spectral Method

AbstractThe fourth order average vector field (AVF) method is applied to solve the “Good” Boussinesq equation. The semi-discrete system of the “good” Boussinesq equation obtained by the pseudo-spectral method in spatial variable, which is a classical finite dimensional Hamiltonian system, is discretizated by the fourth order average vector field method. Thus, a new high order energy conservation scheme of the “good” Boussinesq equation is obtained. Numerical experiments confirm that the new high order scheme can preserve the discrete energy of the “good” Boussinesq equation exactly and simulate evolution of different solitary waves well.

scholarly journals Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation

2005 ◽  
Vol 2005 (6) ◽  
pp. 655-671 ◽  
Author(s):  
Ahmed Y. Abdallah
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Global Attractor ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
Upper Semicontinuity ◽  
Time Variable ◽  
Finite Dimensional ◽  
Lattice Dynamical System ◽  
Second Order In Time

We will study the lattice dynamical system of a nonlinear Boussinesq equation. Our objective is to explore the existence of the global attractor for the solution semiflow of the introduced lattice system and to investigate its upper semicontinuity with respect to a sequence of finite-dimensional approximate systems. As far as we are aware, our result here is the first concerning the lattice dynamical system corresponding to a differential equation of second order in time variable and fourth order in spatial variable with nonlinearity involving the gradients.

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