A Higher Order (2+1)-Dimensional Korteweg-de Vries Equation and Its Exact Solitary Wave Solutions

1990 ◽  
Vol 14 (2) ◽  
pp. 221-224
Author(s):  
Guo-xiang Huang ◽  
Xian-xi Dai ◽  
Sen-yue Lou
Keyword(s):  
Solitary Wave ◽  
Vries Equation ◽  
Higher Order ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries

scholarly journals Travelling Solitary Wave Solutions to Higher Order Korteweg-de Vries Equation

2019 ◽  
Vol 09 (05) ◽  
pp. 354-360
Author(s):  
Chunhuan Xiang ◽  
Honglei Wang
Keyword(s):  
Solitary Wave ◽  
Vries Equation ◽  
Higher Order ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries

On the nonlinear stability of solitary wave solutions of the fifth-order Korteweg–de Vries equation

1999 ◽  
Vol 263 (1-2) ◽  
pp. 98-104 ◽  
Author(s):  
F. Dias ◽  
E.A. Kuznetsov
Keyword(s):  
Solitary Wave ◽  
Nonlinear Stability ◽  
Vries Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries ◽  
Fifth Order

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

2007 ◽  
Vol 16 (12) ◽  
pp. 3589-3594 ◽  
Author(s):  
Yang Hong-Li ◽  
Song Jin-Bao ◽  
Yang Lian-Gui ◽  
Liu Yong-Jun
Keyword(s):  
Solitary Wave ◽  
Vries Equation ◽  
Solitary Wave Solutions ◽  
Interfacial Waves ◽  
Fluid System ◽  
Wave Solutions ◽  
De Vries ◽  
Two Fluid

Analytic Solitary-wave Solutions for Modified Korteweg - de Vries Equation with t-dependent Coefficients

2001 ◽  
Vol 56 (5) ◽  
pp. 366-370 ◽  
Author(s):  
Woo-Pyo Hong ◽  
Myung-Sang Yoona
Keyword(s):  
Solitary Wave ◽  
Symbolic Computation ◽  
Vries Equation ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Modified Kdv Equation ◽  
De Vries ◽  
Truncated Painlevé Expansion

Abstract We find analytic solitary wave solutions for a modified KdV equation with t-dependent coefficients of the form ut - 6α(t)uux + ß (t) uxxx -6γu2ux = 0. We make use of both the application of the truncated Painleve expansion and symbolic computation to obtain an auto-Bäcklund transformation. We show that kink-type analytic solitary-wave solutions exist under some constraints on α (t), ß (t) and γ.

scholarly journals The stability of solitary waves

1972 ◽  
Vol 328 (1573) ◽  
pp. 153-183 ◽  
Keyword(s):  
Solitary Wave ◽  
Spectral Theory ◽  
Solitary Waves ◽  
Vries Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries ◽  
Long Time ◽  
Stability Of Solitary Waves ◽  
The Stability

The Korteweg-de Vries equation, which describes the unidirectional propagation of long waves in a wide class of nonlinear dispersive systems, is well known to have solutions representing solitary waves. The present analysis establishes that these solutions are stable, confirming a property that has for a long time been presumed. The demonstration of stability hinges on two nonlinear functionals which for solutions of the Korteweg-de Vries equation are invariant with time: these are introduced in § 2, where it is recalled that Boussinesq recognized their significance in relation to the stability of solitary waves. The principles upon which the stability theory is based are explained in § 3, being supported by a few elementary ideas from functional analysis. A proof that solitary wave solutions are stable is completed in § 4, the most exacting steps of which are accomplished by means of spectral theory. In appendix A a method deriving from the calculus of variations is presented, whereby results needed for the proof of stability may be obtained independently of spectral theory as used in § 4. In appendix B it is shown how the stability analysis may readily be adapted to solitary-wave solutions of the ‘regularized long-wave equation’ that has recently been advocated by Benjamin, Bona & Mahony as an alternative to the Korteweg-de Vries equation. In appendix C a variational principle is demonstrated relating to the exact boundaryvalue problem for solitary waves in water: this is a counterpart to a principle used in the present work (introduced in §2) and offers some prospect of proving the stability of exact solitary waves.

scholarly journals On solitary wave solutions of the compound Burgers–Korteweg–de Vries equation

2007 ◽  
Vol 375 (1) ◽  
pp. 44-50 ◽  
Author(s):  
Claire David ◽  
Rasika Fernando ◽  
Zhaosheng Feng
Keyword(s):  
Solitary Wave ◽  
Vries Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries

Solitary wave solutions of the compound Burgers–Korteweg–de Vries equation

2005 ◽  
Vol 352 (2-4) ◽  
pp. 419-435 ◽  
Author(s):  
Zhaosheng Feng ◽  
Goong Chen
Keyword(s):  
Solitary Wave ◽  
Vries Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries
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