Travelling wave solutions for the two-dimensional Hirota system of equations

2018 ◽  
Author(s):  
Guldana Bekova ◽  
Gaukhar Shaikhova ◽  
Kuralay Yesmakhanova
Keyword(s):  
Travelling Wave ◽  
System Of Equations ◽  
Travelling Wave Solutions ◽  
Two Dimensional ◽  
Wave Solutions

scholarly journals Asymmetric gravity–capillary solitary waves on deep water

2014 ◽  
Vol 759 ◽  
Author(s):  
Z. Wang ◽  
J.-M. Vanden-Broeck ◽  
P. A. Milewski
Keyword(s):  
Wave Propagation ◽  
Solitary Waves ◽  
Travelling Wave ◽  
Propagation Direction ◽  
Travelling Wave Solutions ◽  
Two Dimensional ◽  
Bifurcation Curve ◽  
Wave Propagation Direction ◽  
Wave Solutions ◽  
Deep Fluid

AbstractWe present new families of gravity–capillary solitary waves propagating on the surface of a two-dimensional deep fluid. These spatially localised travelling-wave solutions are non-symmetric in the wave propagation direction. Our computation reveals that these waves appear from a spontaneous symmetry-breaking bifurcation, and connect two branches of multi-packet symmetric solitary waves. The speed–energy bifurcation curve of asymmetric solitary waves features a zigzag behaviour with one or more turning points.

One- and two-dimensional travelling wave solutions in gas-fluidized beds

1996 ◽  
Vol 306 ◽  
pp. 183-221 ◽  
Author(s):  
B. J. Glasser ◽  
I. G. Kevrekidis ◽  
S. Sundaresan
Keyword(s):  
Fluidized Beds ◽  
Equations Of Motion ◽  
High Amplitude ◽  
Travelling Wave ◽  
Numerical Continuation ◽  
Model Parameters ◽  
Travelling Wave Solutions ◽  
Two Dimensional ◽  
One Dimensional ◽  
Wave Solutions

Making use of numerical continuation techniques as well as bifurcation theory, both one- and two-dimensional travelling wave solutions of the ensemble-averaged equations of motion for gas and particles in fluidized beds have been computed. One-dimensional travelling wave solutions having only vertical structure emerge through a Hopf bifurcation of the uniform state and two-dimensional travelling wave solutions are born out of these one-dimensional waves. Fully developed two-dimensional solutions of high amplitude are reminiscent of bubbles. It is found that the qualitative features of the bifurcation diagram are not affected by changes in model parameters or the closures. An examination of the stability of one-dimensional travelling wave solutions to two-dimensional perturbations suggests that two-dimensional solutions emerge through a mechanism which is similar to the overturning instability analysed by Batchelor & Nitsche (1991).

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