Symmetry classification and exact solutions of (3 + 1)-dimensional fractional nonlinear incompressible non-hydrostatic coupled Boussinesq equations

2021 ◽  
Vol 62 (1) ◽  
pp. 011504
Author(s):  
Komal Singla ◽  
R. K. Gupta
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equations ◽  
Symmetry Classification

scholarly journals On the Variant Boussinesq Equations

1997 ◽  
Vol 52 (4) ◽  
pp. 335-336
Author(s):  
Yi-Tian Gao ◽  
Bo Tian
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Boussinesq Equations ◽  
New Exact Solutions ◽  
Variant Boussinesq Equations

Abstract We extend the generalized tan h method to the variant Boussinesq equations and obtain certain solitary-wave and new exact solutions.

scholarly journals Exact Solutions Superimposed with Nonlinear Plane Waves

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
B. S. Desale ◽  
Vivek Sharma
Keyword(s):  
Exact Solution ◽  
Plane Wave ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Large Scale ◽  
Plane Waves ◽  
Boussinesq Equations ◽  
Integral Curves ◽  
Nonlinear Plane ◽  
Scale Motion

The flow of fluid in atmosphere and ocean is governed by rotating stratified Boussinesq equations. Through the literature, we found that many researchers are trying to find the solutions of rotating stratified Boussinesq equations. In this paper, we have obtained special exact solutions and nonlinear plane waves. Finally, we provide exact solutions to rotating stratified Boussinesq equations with large scale motion superimposed with the nonlinear plane waves. In support of our investigations, we provided two examples: one described the special exact solution and in second example, we have determined the special exact solution superimposed with nonlinear plane wave. Also, we depicted some integral curves that represent the flow of an incompressible fluid particle on the planex1+x2=L(constant)as the particular case.

Similarity reductions and exact solutions for two-dimensional Euler–Boussinesq equations

2019 ◽  
Vol 33 (27) ◽  
pp. 1950328
Author(s):  
En Gui Fan ◽  
Man Wai Yuen
Keyword(s):  
Exact Solutions ◽  
Stream Function ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Two Dimensional ◽  
Similarity Reduction ◽  
Wave Solutions ◽  
Similarity Reductions

In this paper, by introducing a stream function and new coordinates, we transform classical Euler–Boussinesq equations into a vorticity form. We further construct traveling wave solutions and similarity reduction for the vorticity form of Euler–Boussinesq equations. In fact, our similarity reduction provides a kind of linearization transformation of Euler–Boussinesq equations.

scholarly journals Exact Solutions of Damped Improved Boussinesq Equations by Extended (G′/G)-Expansion Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Kai Fan ◽  
Cunlong Zhou
Keyword(s):  
Exact Solutions ◽  
Fluid Dynamic ◽  
Boussinesq Equations ◽  
Expansion Method ◽  
Travelling Wave ◽  
Auxiliary Function ◽  
Existence Of A Solution ◽  
Hydrodynamic Damping ◽  
Kink Wave ◽  
Physical Phenomena

With the help of the auxiliary function method, we solved the improved Boussinesq (IBq) equation with fluid dynamic damping and the modified IBq (IMBq) equation with Stokes damping, and we obtained their three types of travelling wave exact solutions, which is an extension service of the numerical simulation and the existence of a solution. From the waveform diagram of IBq equation with hydrodynamic damping, it can be seen that when the propagation velocity of kink wave changes, the amplitude also changes significantly, and it is also found that the kink isolated waveform is significantly asymmetric due to the increase of damping coefficient v, which may be of some value in explaining some physical phenomena. In addition, the symbolic computing software maple makes our computing work easier.

Symmetry classification and exact solutions of the Kramers equation

1998 ◽  
Vol 39 (6) ◽  
pp. 3505-3510 ◽  
Author(s):  
Stanislav Spichak ◽  
Valerii Stognii
Keyword(s):  
Exact Solutions ◽  
Symmetry Classification ◽  
Kramers Equation

The Structures and the Interactions of Soliton in two (2+1)-dimensional KdV-Type Equations

2004 ◽  
Vol 59 (1-2) ◽  
pp. 14-22
Author(s):  
Hang-yu Ruan
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equations ◽  
Repulsive Interaction ◽  
Bilinear Method ◽  
Breather Solution ◽  
Kdv Type Equations ◽  
Line Soliton

Exact solutions in two (2+1)-dimensional KdV-type (Sawada-Kodera and Boussinesq) equations are presented by using the bilinear method. The N-breather solution, the solution to describe the interaction between a line soliton and a y-periodic soliton, and the solution to express the interaction between two y-periodic solitons are included in our results. Detailed behavior of interactions between a line soliton and a y-periodic soliton for the SK equation and between two y-periodic solitons for the BS equation are illustrated both analytically and graphically. For these two equations, we only discuss the repulsive interaction keeping the shapes of the soliton unchanged.

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