THE GENERALIZED WRONSKIAN SOLUTIONS OF THE INTEGRABLE VARIABLE-COEFFICIENT KORTEWEG-DE VRIES EQUATION

2011 ◽  
Vol 25 (32) ◽  
pp. 4615-4626 ◽  
Author(s):  
YI ZHANG ◽  
HAI-QIONG ZHAO ◽  
LING-YA YE ◽  
YI-NENG LV
Keyword(s):  
Fluid Dynamics ◽  
Exact Solutions ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Sufficient Conditions ◽  
Rational Solutions ◽  
Wronskian Determinant ◽  
Linear Partial Differential Equations ◽  
De Vries ◽  
Bose Einstein

A broad set of sufficient conditions consisting of systems of linear partial differential equations are presented which guarantee that the Wronskian determinant is the solutions of the integrable variable-coefficient Korteweg-de Vries model from Bose–Einstein condensates and fluid dynamics. The generalized Wronskian solutions provide us with a comprehensive approach to construct many exact solutions including rational solutions, solitons, negatons, positons, and complexitons.

Non-linear Dynamics and Exact Solutions for the Variable-Coefficient Modified Korteweg–de Vries Equation

2018 ◽  
Vol 73 (2) ◽  
pp. 143-149 ◽  
Author(s):  
Jiangen Liu ◽  
Yufeng Zhang
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Rational Solutions ◽  
Transformation Technique ◽  
Linear Dynamics ◽  
New Exact Solutions ◽  
Non Linear ◽  
De Vries

AbstractThis paper presents some new exact solutions which contain soliton solutions, breather solutions and two types of rational solutions for the variable-coefficient-modified Korteweg–de Vries equation, with the help of the multivariate transformation technique. Furthermore, based on these new soliton solutions, breather solutions and rational solutions, we discuss their non-linear dynamics properties. We also show the graphic illustrations of these solutions which can help us better understand the evolution of solution waves.

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

scholarly journals Two Different Classes of Wronskian Conditions to a (3 + 1)-Dimensional Generalized Shallow Water Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Yaning Tang ◽  
Pengpeng Su
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Sufficient Conditions ◽  
Wronskian Technique ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Wronskian Determinant ◽  
Linear Partial Differential Equations ◽  
Hirota Bilinear Equation ◽  
Hirota Bilinear

Based on the Hirota bilinear method and Wronskian technique, two different classes of sufficient conditions consisting of linear partial differential equations system are presented, which guarantee that the Wronskian determinant is a solution to the corresponding Hirota bilinear equation of a (3+1)-dimensional generalized shallow water equation. Our results show that the nonlinear equation possesses rich and diverse exact solutions such as rational solutions, solitons, negatons, and positons.

N-Solitonic Solution in Terms of Wronskian Determinant for a Perturbed Variable-Coefficient Korteweg-de Vries Equation

2007 ◽  
Vol 47 (2) ◽  
pp. 553-560 ◽  
Author(s):  
Cheng Zhang ◽  
Hong-Wu Zhu ◽  
Chun-Yi Zhang ◽  
Zhen-Zhi Yao ◽  
Xing Lü ◽  
...  
Keyword(s):  
Variable Coefficient ◽  
Vries Equation ◽  
Wronskian Determinant ◽  
Solitonic Solution ◽  
De Vries

scholarly journals Painleve analysis for a forced Korteveg-de Vries equation arisen in fluid dynamics of internal solitary waves

2015 ◽  
Vol 19 (4) ◽  
pp. 1223-1226 ◽  
Author(s):  
Sheng Zhang ◽  
Mei-Tong Chen ◽  
Wei-Yi Qian
Keyword(s):  
Fluid Dynamics ◽  
Solitary Waves ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Internal Solitary Waves ◽  
Painlevé Analysis ◽  
New Exact Solutions ◽  
De Vries ◽  
Painleve Analysis ◽  
Truncated Painlevé Expansion

In this paper, Painleve analysis is used to test the Painleve integrability of a forced variable-coefficient extended Korteveg-de Vries equation which can describe the weakly-non-linear long internal solitary waves in the fluid with continuous stratification on density. The obtained results show that the equation is integrable under certain conditions. By virtue of the truncated Painleve expansion, a pair of new exact solutions to the equation is obtained.

Integrable properties of a variable-coefficient Korteweg–de Vries model from Bose–Einstein condensates and fluid dynamics

2006 ◽  
Vol 39 (46) ◽  
pp. 14353-14362 ◽  
Author(s):  
Chun-Yi Zhang ◽  
Yi-Tian Gao ◽  
Xiang-Hua Meng ◽  
Juan Li ◽  
Tao Xu ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Variable Coefficient ◽  
De Vries ◽  
Bose Einstein
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