scholarly journals Higher Order Exponential Splittings for the Fast Non-Linear Fourier Transform of the Korteweg-De Vries Equation

2018 ◽  
Author(s):  
Peter J. Prins ◽  
Sander Wahls
Keyword(s):  
Fourier Transform ◽  
Vries Equation ◽  
Higher Order ◽  
Non Linear ◽  
De Vries

scholarly journals New Cubic B-spline Approximations for Solving Non-linear Third-order Korteweg-de Vries Equation

2019 ◽  
Vol 12 (6) ◽  
pp. 1-9
Author(s):  
Muhammad Abbas ◽  
Muhammad Kashif Iqbal ◽  
Bushra Zafar ◽  
Shazalina Binti Mat Zin ◽  
◽  
...  
Keyword(s):  
Vries Equation ◽  
Third Order ◽  
B Spline ◽  
Non Linear ◽  
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.

Residual Symmetries and Interaction Solutions for the Classical Korteweg-de Vries Equation

2017 ◽  
Vol 72 (3) ◽  
pp. 217-222 ◽  
Author(s):  
Jin-Xi Fei ◽  
Wei-Ping Cao ◽  
Zheng-Yi Ma
Keyword(s):  
Vries Equation ◽  
Expansion Method ◽  
Point Symmetry ◽  
Residual Symmetry ◽  
Interaction Solutions ◽  
Dependent Variables ◽  
Non Linear ◽  
De Vries ◽  
Finite Transformation ◽  
Non Local

AbstractThe non-local residual symmetry for the classical Korteweg-de Vries equation is derived by the truncated Painlevé analysis. This symmetry is first localised to the Lie point symmetry by introducing the auxiliary dependent variables. By using Lie’s first theorem, we then obtain the finite transformation for the localised residual symmetry. Based on the consistent tanh expansion method, some exact interaction solutions among different non-linear excitations are explicitly presented finally. Some special interaction solutions are investigated both in analytical and graphical ways at the same time.

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.

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