Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method

2001 ◽  
Vol 12 (8) ◽  
pp. 1549-1556 ◽  
Author(s):  
A.M. Wazwaz
Keyword(s):  
Periodic Solutions ◽  
Decomposition Method ◽  
Boussinesq Equation ◽  
Soliton Solutions

On soliton solutions of the (2+1) dimensional Boussinesq equation

2012 ◽  
Vol 219 (8) ◽  
pp. 3414-3419 ◽  
Author(s):  
A.S. Abdel Rady ◽  
E.S. Osman ◽  
Mohammed Khalfallah
Keyword(s):  
Boussinesq Equation ◽  
Soliton Solutions

The integrable Boussinesq equation and it’s breather, lump and soliton solutions

2022 ◽  
Author(s):  
Sachin Kumar ◽  
Sandeep Malik ◽  
Hadi Rezazadeh ◽  
Lanre Akinyemi
Keyword(s):  
Boussinesq Equation ◽  
Soliton 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.

SOLITON INTERACTIONS FOR THE GENERALIZED (3+1)-DIMENSIONAL BOUSSINESQ EQUATION

2012 ◽  
Vol 26 (07) ◽  
pp. 1250062 ◽  
Author(s):  
XIAO-LING GAI ◽  
YI-TIAN GAO ◽  
XIN YU ◽  
ZHI-YUAN SUN
Keyword(s):  
Soliton Solution ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Analytic Solutions ◽  
Propagation Process ◽  
Soliton Propagation ◽  
Soliton Interactions ◽  
Pass Through ◽  
The Moment ◽  
The One

Generalized (3+1)-dimensional Boussinesq equation is investigated in this paper. Through the dependent variable transformation and symbolic computation, the one- and two-soliton solutions are obtained. With the one-soliton solution, the coefficient effects in the soliton propagation process are investigated. Through analyzing the two-soliton solution, two kinds of two-soliton interactions are presented: (i) Two solitons merge into a bigger one whose amplitude increases but does not exceed the sum of the two at the moment of the collision; (ii) Two solitons can pass through each other, and their shapes keep unchanged with a phase shift after the separation. In addition, two kinds of analytic solutions are discussed: (i) "Amplitudes" of the two analytic solutions immediately turn to negative (positive) infinity after the "collision"; (ii) Two analytic solutions are fused into a higher peak (valley) at the moment of "collision", whose "amplitudes" change to negative (positive) infinity after the separation.

scholarly journals Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Alvaro H. Salas S ◽  
Cesar A. Gómez S
Keyword(s):  
Exact Solutions ◽  
Periodic Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Third Order ◽  
Forcing Term ◽  
Projective Riccati Equation Method

The general projective Riccati equation method and the Exp-function method are used to construct generalized soliton solutions and periodic solutions to special KdV equation with variable coefficients and forcing term.

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