scholarly journals Subharmonic dynamics of wave trains in the Korteweg‐de Vries/Kuramoto‐Sivashinsky equation

2021 ◽  
Author(s):  
Mathew A. Johnson ◽  
Wesley R. Perkins
Keyword(s):  
De Vries ◽  
Wave Trains ◽  
Sivashinsky Equation

Cnoidal Wave Trains and Solitary Waves in a Dissipation-Modified Korteweg—de Vries Equation

KdV ’95 ◽  
1995 ◽  
pp. 457-475
Author(s):  
A. Ye. Rednikov ◽  
M. G. Velarde ◽  
Yu. S. Ryazantsev ◽  
A. A. Nepomnyashchy ◽  
V. N. Kurdyumov
Keyword(s):  
Solitary Waves ◽  
Vries Equation ◽  
Cnoidal Wave ◽  
De Vries ◽  
Wave Trains

Cnoidal wave trains and solitary waves in a dissipation-modified Korteweg-de Vries equation

1995 ◽  
Vol 39 (1-3) ◽  
pp. 457-475 ◽  
Author(s):  
A. Ye. Rednikov ◽  
M. G. Velarde ◽  
Yu. S. Ryazantsev ◽  
A. A. Nepomnyashchy ◽  
V. N. Kurdyumov
Keyword(s):  
Solitary Waves ◽  
Vries Equation ◽  
Cnoidal Wave ◽  
De Vries ◽  
Wave Trains

SOLITARY WAVES, SOLITON BOUND STATES AND CHAOS IN A DISSIPATIVE KORTEWEG-DE VRIES EQUATION

1994 ◽  
Vol 04 (05) ◽  
pp. 1135-1146 ◽  
Author(s):  
VLADIMIR I. NEKORKIN ◽  
MANUEL G. VELARDE
Keyword(s):  
Internal Waves ◽  
Solitary Waves ◽  
Liquid Layer ◽  
Bound States ◽  
Vries Equation ◽  
Stratified Fluid ◽  
Localized Structures ◽  
Fluid Layers ◽  
De Vries ◽  
Wave Trains

Propagating dissipative (localized) structures like solitary waves, pulses or “solitons,” “bound solitons,” and “chaotic” wave trains are shown to be solutions of a dissipation-modified Korteweg-de Vries equation that in particular appears in Marangoni-Bénard convection when a liquid layer is heated from the air side and in the description of internal waves in sheared, stably stratified fluid layers.

scholarly journals WELL-POSEDNESS FOR A FAMILY OF PERTURBATIONS OF THE KdV EQUATION IN PERIODIC SOBOLEV SPACES OF NEGATIVE ORDER

2013 ◽  
Vol 15 (06) ◽  
pp. 1350005
Author(s):  
XAVIER CARVAJAL PAREDES ◽  
RICARDO A. PASTRAN
Keyword(s):  
Sobolev Spaces ◽  
Initial Value Problem ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Well Posedness ◽  
Initial Value ◽  
Negative Order ◽  
The Kdv Equation ◽  
De Vries ◽  
Sivashinsky Equation

We establish local well-posedness in Sobolev spaces Hs(𝕋), with s ≥ -1/2, for the initial value problem issues of the equation [Formula: see text] where η > 0, (Lu)∧(k) = -Φ(k)û(k), k ∈ ℤ and Φ ∈ ℝ is bounded above. Particular cases of this problem are the Korteweg–de Vries–Burgers equation for Φ(k) = -k2, the derivative Korteweg–de Vries–Kuramoto–Sivashinsky equation for Φ(k) = k2 - k4, and the Ostrovsky–Stepanyams–Tsimring equation for Φ(k) = |k| - |k|3.

FURTHER RESULTS ON THE EVOLUTION OF SOLITARY WAVES AND THEIR BOUND STATES OF A DISSIPATIVE KORTEWEG-DE VRIES EQUATION

1995 ◽  
Vol 05 (03) ◽  
pp. 831-839 ◽  
Author(s):  
MANUEL G. VELARDE ◽  
VLADIMIR I. NEKORKIN ◽  
ANDREY G. MAKSIMOV
Keyword(s):  
Solitary Waves ◽  
Bound States ◽  
Marangoni Convection ◽  
Vries Equation ◽  
Dissipative Structures ◽  
Long Wavelength ◽  
Numerical Evidence ◽  
De Vries ◽  
Wave Trains

Numerical evidence is provided of (long lasting) solitary waves (traveling localized dissipative structures) and their bound states as well as periodic and “chaotic”, erratic wave trains of a dissipation-modified Korteweg-de Vries equation originally derived to account for long wavelength oscillatory Bénard-Marangoni convection.

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