The Korteweg-de Vries Equation with Small Dispersion: Higher Order Lax-Levermore Theory

1991 ◽  
pp. 255-262
Author(s):  
Stephanos Venakides
Keyword(s):  
Vries Equation ◽  
Higher Order ◽  
De Vries ◽  
Small Dispersion

Gauge transformation and the higher order Korteweg–de Vries equation

1988 ◽  
Vol 29 (2) ◽  
pp. 308-314 ◽  
Author(s):  
Yu‐kun Zheng ◽  
W. L. Chan
Keyword(s):  
Gauge Transformation ◽  
Vries Equation ◽  
Higher Order ◽  
De Vries

Noncommutative coupled complex modified Korteweg–de Vries equation: Darboux and binary Darboux transformations

2019 ◽  
Vol 34 (07n08) ◽  
pp. 1950054
Author(s):  
H. Wajahat A. Riaz
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Nonlinear Evolution Equations ◽  
Order Effects ◽  
Darboux Transformations ◽  
De Vries ◽  
Higher Order Effects

Higher-order nonlinear evolution equations are important for describing the wave propagation of second- and higher-order number of fields in optical fiber systems with higher-order effects. One of these equations is the coupled complex modified Korteweg–de Vries (ccmKdV) equation. In this paper, we study noncommutative (nc) generalization of ccmKdV equation. We present Darboux and binary Darboux transformations (DTs) for the nc-ccmKdV equation and then construct its Quasi-Grammian solutions. Further, single and double-hump soliton solutions of first- and second-order are given in commutative settings.

Double-soliton and conservation law structures for a higher-order type of Korteweg-de Vries equation

2015 ◽  
Vol 28 (4) ◽  
pp. 633-638
Author(s):  
C. T. Lee ◽  
C. C. Lee ◽  
M. L. Liu
Keyword(s):  
Conservation Law ◽  
Vries Equation ◽  
Order Type ◽  
Higher Order ◽  
De Vries
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