Spontaneous soliton generation in the higher order Korteweg–de Vries equations on the half-line

2012 ◽  
Vol 22 (1) ◽  
pp. 013138
Author(s):  
G. I. Burde
Keyword(s):  
Higher Order ◽  
Half Line ◽  
De Vries ◽  
Soliton Generation

The tanh and sine–cosine methods for higher order equations of Korteweg–de Vries type

2011 ◽  
Vol 84 (2) ◽  
pp. 025010 ◽  
Author(s):  
Marwan Alquran ◽  
Kamel Al-Khaled
Keyword(s):  
Higher Order ◽  
De Vries

The Neumann and Robin problems for the Korteweg–de Vries equation on the half-line

2021 ◽  
Vol 62 (11) ◽  
pp. 111503
Author(s):  
A. Alexandrou Himonas ◽  
Carlos Madrid ◽  
Fangchi Yan
Keyword(s):  
Vries Equation ◽  
Half Line ◽  
De Vries

scholarly journals Higher-order Darboux transformations for two-dimensional Dirac systems with diagonal matrix potential

2021 ◽  
Vol 2090 (1) ◽  
pp. 012038
Author(s):  
A Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Explicit Form ◽  
Higher Order ◽  
Diagonal Matrix ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Systems ◽  
Matrix Potential ◽  
De Vries ◽  
The Matrix

Abstract We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

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.

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