scholarly journals Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations

2020 ◽  
Author(s):  
Jerry L. Bona ◽  
Angel Durán ◽  
Dimitrios Mitsotakis
Keyword(s):  
Solitary Wave ◽  
Internal Waves ◽  
Solitary Wave Solutions ◽  
Wave Solutions

No description supplied

The stability of internal solitary waves

1983 ◽  
Vol 94 (2) ◽  
pp. 351-379 ◽  
Author(s):  
D. P. Bennett ◽  
R. W. Brown ◽  
S. E. Stansfield ◽  
J. D. Stroughair ◽  
J. L. Bona
Keyword(s):  
Solitary Wave ◽  
Internal Waves ◽  
Solitary Waves ◽  
Model Equation ◽  
Focus Of Attention ◽  
Internal Solitary Waves ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Stability ◽  
The One

A theory is developed relating to the stability of solitary-wave solutions of the so-called Benjamin-Ono equation. This equation was derived by Benjamin (5) as a model for the propagation of internal waves in an incompressible non-diffusive heterogeneous fluid for which the density is non-constant only within a layer whose thickness is much smaller than the total depth. In his article, Benjamin wrote in closed form the one-parameter family of solitary-wave solutions of his model equation whose stability will be the focus of attention presently.

scholarly journals Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations

2020 ◽  
Author(s):  
Jerry L. Bona ◽  
Angel Durán ◽  
Dimitrios Mitsotakis
Keyword(s):  
Solitary Wave ◽  
Internal Waves ◽  
Solitary Wave Solutions ◽  
Wave Solutions

No description supplied

scholarly journals Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations

2021 ◽  
Vol 41 (1) ◽  
pp. 87-111
Author(s):  
Jerry L. Bona ◽  
◽  
Angel Durán ◽  
Dimitrios Mitsotakis ◽  
◽  
...  
Keyword(s):  
Solitary Wave ◽  
Internal Waves ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Internal wave shoaling in nearly linear stratifications

2021 ◽  
Author(s):  
Marek Stastna ◽  
Kevin Lamb
Keyword(s):  
Solitary Wave ◽  
Internal Waves ◽  
Solitary Waves ◽  
Coastal Ocean ◽  
Internal Solitary Waves ◽  
Solitary Wave Solutions ◽  
Nonlinearity Coefficient ◽  
Weak Nonlinearity ◽  
Wave Solutions ◽  
Wave Shoaling

<div> <div> <div> <p>In the theory of internal waves in the coastal ocean, linear stratification plays an exceptional role. This is because the nonlinearity coefficient in KdV theory vanishes, and in the case of large amplitude waves, the DJL theory linearizes and fails to give solitary wave solutions. We consider small, physically consistent perturbations of a linearly stratified fluid that would result from a localized mixing near a particular depth. We demonstrate that the DJL equation does yield exact internal solitary waves in this case. These waves are long due to the weak nonlinearity, and we explore how this weak nonlinearity manifests during shoaling.</p> </div> </div> </div>

scholarly journals On solitary-wave solutions of Boussinesq/Boussinesq systems for internal waves

2021 ◽  
Vol 428 ◽  
pp. 133051
Author(s):  
Vassilios A. Dougalis ◽  
Angel Durán ◽  
Leetha Saridaki
Keyword(s):  
Solitary Wave ◽  
Internal Waves ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Boussinesq Systems
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