Solitary wave solution of higher-order Korteweg–de Vries equation

2009 ◽  
Vol 39 (1) ◽  
pp. 277-281 ◽  
Author(s):  
Jnanjyoti Sarma
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Vries Equation ◽  
Solitary Wave Solution ◽  
Higher Order ◽  
De Vries

Periodic Wave Solutions of a Generalized KdV-mKdV Equation with Higher-Order Nonlinear Terms

2010 ◽  
Vol 65 (8-9) ◽  
pp. 649-657 ◽  
Author(s):  
Zi-Liang Li
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Higher Order ◽  
Periodic Wave Solution ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
De Vries ◽  
Ode Method

The Jacobin doubly periodic wave solution, the Weierstrass elliptic function solution, the bell-type solitary wave solution, the kink-type solitary wave solution, the algebraic solitary wave solution, and the triangular solution of a generalized Korteweg-de Vries-modified Korteweg-de Vries equation (GKdV-mKdV) with higher-order nonlinear terms are obtained by a generalized subsidiary ordinary differential equation method (Gsub-ODE method for short). The key ideas of the Gsub-ODE method are that the periodic wave solutions of a complicated nonlinear wave equation can be constructed by means of the solutions of some simple and solvable ODE which are called Gsub-ODE with higherorder nonlinear terms

scholarly journals Exact dipole solitary wave solution in metamaterials with higher-order dispersion

2016 ◽  
Vol 63 (sup3) ◽  
pp. S44-S50 ◽  
Author(s):  
Xuemin Min ◽  
Rongcao Yang ◽  
Jinping Tian ◽  
Wenrui Xue ◽  
J. M. Christian
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Higher Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

Transcritical flow over obstacles and holes: forced Korteweg–de Vries framework

2019 ◽  
Vol 881 ◽  
pp. 660-678 ◽  
Author(s):  
Roger H. J. Grimshaw ◽  
Montri Maleewong
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Vries Equation ◽  
Solitary Wave Solution ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Main Concern ◽  
Oncoming Flow ◽  
Transcritical Flow ◽  
De Vries

This paper extends a previous study of free-surface flow over two localised obstacles using the framework of the forced Korteweg–de Vries equation, to an analogous study of flow over two localised holes, or a combination of an obstacle and a hole. Importantly the terminology obstacle or hole can be reversed for a stratified fluid and refers more precisely to the relative polarity of the forcing and the solitary wave solution of the unforced Korteweg–de Vries equation. As in the previous study, our main concern is with the transcritical regime when the oncoming flow has a Froude number close to unity. In the transcritical regime at early times, undular bores are produced upstream and downstream of each forcing site. We then describe the interaction of these undular bores between the forcing sites, and the outcome at very large times.

Solitary wave solution to a class of higher-order viscous traffic flow model

2017 ◽  
Vol 31 (13) ◽  
pp. 1750099 ◽  
Author(s):  
Chun-Xiu Wu ◽  
Peng Zhang
Keyword(s):  
Solitary Wave ◽  
Traffic Flow ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Higher Order ◽  
Order Accuracy ◽  
Flow Models ◽  
Weighted Essentially Nonoscillatory ◽  
Traffic Flow Models ◽  
Fifth Order

Traveling waves of a class of higher-order traffic flow models with viscosity are studied with the reduction perturbation method, which leads to the well-known Kortweg–de Vries equation and the approximate solitary wave solution to the model. The fifth-order accuracy weighted essentially nonoscillatory scheme is adopted for comparison between the analytical and numerical results. The numerical tests show that the solitary wave evolves with little deformation of its profile and that a globally perturbed equilibrium traffic state is able to evolve into a profile similar to that of a solitary wave, which is identified by the same total number of vehicles on the ring road. These results are compared with those in the literature and demonstrate that the approximation to the model is more accurate.

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