Solutons of a nonisospectral and variable coefficient Korteweg-de Vries equation

1987 ◽  
Vol 14 (4) ◽  
pp. 293-301 ◽  
Author(s):  
W. L. Chan ◽  
Zheng Yu-Kun
Keyword(s):  
Variable Coefficient ◽  
Vries Equation ◽  
De Vries

Wronskian solutions and integrability for a generalized variable-coefficient forced Korteweg–de Vries equation in fluids

2011 ◽  
Vol 67 (2) ◽  
pp. 1023-1030 ◽  
Author(s):  
Xin Yu ◽  
Yi-Tian Gao ◽  
Zhi-Yuan Sun ◽  
Ying Liu
Keyword(s):  
Variable Coefficient ◽  
Vries Equation ◽  
De Vries

Ablowitz–Kaup–Newell–Segur system, conservation laws and Bäcklund transformation of a variable-coefficient Korteweg–de Vries equation in plasma physics, fluid dynamics or atmospheric science

2020 ◽  
Vol 34 (25) ◽  
pp. 2050226 ◽  
Author(s):  
Yu-Qi Chen ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
He Li ◽  
Xue-Hui Zhao ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Bäcklund Transformation ◽  
Atmospheric Science ◽  
Backlund Transformation ◽  
Atmospheric Flow ◽  
Bilinear Bäcklund Transformation ◽  
De Vries ◽  
Nonlinearity Dispersion

For a variable-coefficient Korteweg–de Vries equation in a lake/sea, two-layer liquid, atmospheric flow, cylindrical plasma or interactionless plasma, in this paper, we derive the bilinear Bäcklund transformation, non-isospectral Ablowitz–Kaup–Newell–Segur system and infinite conservation laws for the wave amplitude under certain constraints among the external force, dissipation, nonlinearity, dispersion and perturbation.

Solitons for a forced generalized variable-coefficient Korteweg–de Vries equation for the atmospheric blocking phenomenon

2016 ◽  
Vol 30 (35) ◽  
pp. 1650318 ◽  
Author(s):  
Jun Chai ◽  
Bo Tian ◽  
Xi-Yang Xie ◽  
Han-Peng Chai
Keyword(s):  
Variable Coefficient ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Atmospheric Blocking ◽  
Graphic Analysis ◽  
Bilinear Bäcklund Transformation ◽  
Different Types ◽  
De Vries ◽  
Soliton Amplitude ◽  
The One

Investigation is given to a forced generalized variable-coefficient Korteweg–de Vries equation for the atmospheric blocking phenomenon. Applying the double-logarithmic and rational transformations, respectively, under certain variable-coefficient constraints, we get two different types of bilinear forms: (a) Based on the first type, the bilinear Bäcklund transformation (BT) is derived, the [Formula: see text]-soliton solutions in the Wronskian form are constructed, and the [Formula: see text]- and [Formula: see text]-soliton solutions are proved to satisfy the bilinear BT; (b) Based on the second type, via the Hirota method, the one- and two-soliton solutions are obtained. Those two types of solutions are different. Graphic analysis on the two types shows that the soliton velocity depends on [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the soliton amplitude is merely related to [Formula: see text], and the background depends on [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are the dissipative, dispersive, nonuniform and line-damping coefficients, respectively, and [Formula: see text] is the external-force term. We present some types of interactions between the two solitons, including the head-on and overtaking interactions, interactions between the velocity- and amplitude-unvarying two solitons, between the velocity-varying while amplitude-unvarying two solitons and between the velocity- and amplitude-varying two solitons, as well as the interactions occurring on the constant and varying backgrounds.

scholarly journals Multi-wave solutions for a non-isospectral KDV-type equation with variable coefficients

2012 ◽  
Vol 16 (5) ◽  
pp. 1476-1479 ◽  
Author(s):  
Sheng Zhang ◽  
Qun Gao ◽  
Qian-An Zong ◽  
Dong Liu
Keyword(s):  
Variable Coefficient ◽  
Function Method ◽  
Evolution Equations ◽  
Vries Equation ◽  
Type Equation ◽  
Variable Coefficients ◽  
Linear Evolution ◽  
Wave Solutions ◽  
De Vries ◽  
Linear Evolution Equations

As a typical mathematical model in fluids and plasmas, Korteweg-de Vries equation is famous. In this paper, the Exp-function method is extended to a nonisos-pectral Korteweg-de Vries type equation with three variable coefficients, and multi-wave solutions are obtained. It is shown that the Expfunction method combined with appropriate ansatz may provide with a straightforward, effective and alternative method for constructing multi-wave solutions of variable-coefficient non-linear evolution equations.

Periodic and rational solutions of variable-coefficient modified Korteweg–de Vries equation

2017 ◽  
Vol 89 (1) ◽  
pp. 617-622 ◽  
Author(s):  
Ritu Pal ◽  
Harleen Kaur ◽  
Thokala Soloman Raju ◽  
C. N. Kumar
Keyword(s):  
Variable Coefficient ◽  
Vries Equation ◽  
Rational Solutions ◽  
De Vries
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