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.

scholarly journals Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface

2002 ◽  
Vol 9 (3/4) ◽  
pp. 221-235 ◽  
Author(s):  
R. Grimshaw ◽  
E. Pelinovsky ◽  
O. Poloukhina
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Solitary Waves ◽  
Vries Equation ◽  
Wave Theory ◽  
Higher Order ◽  
Internal Solitary Waves ◽  
Long Wave ◽  
De Vries ◽  
Stratified Shear Flow

Abstract. A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation.

The prolongation structure of a higher order Korteweg-de Vries equation

1978 ◽  
Vol 358 (1694) ◽  
pp. 287-296 ◽  
Keyword(s):  
Lie Algebra ◽  
Vries Equation ◽  
Higher Order ◽  
De Vries ◽  
Prolongation Structure

We have used Wahlquist & Estabrook’s prolongation method to construct a Lie algebra for the higher order Korteweg de Vries (K.deV.) equation q 4 x + α qq 2 x + β q 2 x + γ q 3 ) x + q t = 0 with ( q nx =

scholarly journals HIGHER ORDER KORTEWEG-DE VRIES MODELS FOR INTERNAL WAVES

2003 ◽  
Vol 2 (2) ◽  
pp. 15
Author(s):  
J. JAHARUDDIN
Keyword(s):  
Free Surface ◽  
Evolution Equation ◽  
Linear Theory ◽  
Internal Waves ◽  
Solvability Condition ◽  
Vries Equation ◽  
Asymptotic Methods ◽  
Higher Order ◽  
De Vries ◽  
Order Extension

By using asymptotic methods, evolution equation is derived for the internal waves in density stratified fluid. This evo- lution equation arise as a solvability condition. A higher-order extension of the familiar Korteweg-de Vries equation is produced for internal waves in a density stratified flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed via integrals of the modal function for the linear theory of long internal waves.

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