A Model Equation Illustrating Subcritical Instability to Long Waves in Shear Flows

1987 ◽  
Vol 76 (3) ◽  
pp. 265-275
Author(s):  
I. H. Herron ◽  
S. A. Maslowe ◽  
S. Melkonian
Keyword(s):  
Model Equation ◽  
Shear Flows ◽  
Long Waves ◽  
Subcritical Instability

On the stability theory of solitary waves

1975 ◽  
Vol 344 (1638) ◽  
pp. 363-374 ◽  
Keyword(s):  
Solitary Waves ◽  
Stability Theory ◽  
Alternative Model ◽  
Model Equation ◽  
Vries Equation ◽  
Long Waves ◽  
Dispersive Media ◽  
Stability Of Solitary Waves ◽  
The Stability

Improvements are made on the theory for the stability of solitary waves developed by T. B. Benjamin. The results apply equally to the Kortewegde Vries equation and to an alternative model equation for the propagation of long waves in nonlinear dispersive media.

Second order resonance and subcritical instability

1975 ◽  
Vol 343 (1634) ◽  
pp. 351-362 ◽  
Keyword(s):  
Nonlinear Stability ◽  
Shear Flows ◽  
Single Mode ◽  
Second Order ◽  
Stability Criteria ◽  
Subcritical Instability ◽  
Order Resonance

The role of second order resonance among wavelike disturbances is examined with reference to the subcritical stability or instability of shear flows. Nonlinear stability criteria are derived which may often improve upon the ‘single-mode’ criterion of Stuart (i960) and Joseph & Sattinger 1972).

Another possible model equation for long waves in nonlinear dispersive systems

1977 ◽  
Vol 61 (7) ◽  
pp. 429-430 ◽  
Author(s):  
Richard I. Joseph ◽  
Robert Egri
Keyword(s):  
Model Equation ◽  
Long Waves ◽  
Dispersive Systems

Soliton solutions in different classes for the Kaup–Newell model equation

2019 ◽  
Vol 34 (03) ◽  
pp. 2050038 ◽  
Author(s):  
Abbagari Souleymanou ◽  
Alper Korkmaz ◽  
Hadi Rezazadeh ◽  
Serge Paulin Takougoum Mukam ◽  
Ahmet Bekir
Keyword(s):  
Magnetic Fields ◽  
Exact Solutions ◽  
Model Equation ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Riccati Equations ◽  
Long Waves ◽  
Related Literature ◽  
Triangular Function

In this paper, we use the new defined direct algebraic method based on some particular Riccati equations to find exact solutions to a Kaup–Newell model equation. Several new solutions which represent long waves parallel to the magnetic fields have been obtained. Many solutions in generalized hyperbolic and triangular function forms, exponential or logarithmic, are expressed explicitly. Most of the solutions determined in the study are new in the related literature.

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