scholarly journals Painleve analysis, Auto-Backlund transformation and new exact solutions for improved modied KdV equation

2014 ◽  
Vol 3 (3) ◽  
Author(s):  
Omar H. El-Kalaawy ◽  
R. B. Aldenari
Keyword(s):  
Exact Solutions ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Painlevé Analysis ◽  
Backlund Transformation ◽  
New Exact Solutions ◽  
Painleve Analysis

scholarly journals Bäcklund Transformation and New Exact Solutions of the Sharma-Tasso-Olver Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Lin Jianming ◽  
Ding Jie ◽  
Yuan Wenjun
Keyword(s):  
Exact Solutions ◽  
Bäcklund Transformation ◽  
Analytic Study ◽  
Bäcklund Transformations ◽  
Painlevé Analysis ◽  
Backlund Transformation ◽  
New Exact Solutions ◽  
Backlund Transformations ◽  
Painleve Analysis

The Sharma-Tasso-Olver (STO) equation is investigated. The Painlevé analysis is efficiently used for analytic study of this equation. The Bäcklund transformations and some new exact solutions are formally derived.

AUTO-BÄCKLUND TRANSFORMATION AND NEW EXACT SOLUTIONS OF THE (2 + 1)-DIMENSIONAL NIZHNIK–NOVIKOV–VESELOV EQUATION

2005 ◽  
Vol 16 (03) ◽  
pp. 393-412 ◽  
Author(s):  
DENGSHAN WANG ◽  
HONG-QING ZHANG
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Bäcklund Transformation ◽  
Rational Solution ◽  
Expansion Method ◽  
Backlund Transformation ◽  
Paper Making ◽  
New Exact Solutions ◽  
Physical Phenomena ◽  
Series Expansion Method

In this paper, making use of the truncated Laurent series expansion method and symbolic computation we get the auto-Bäcklund transformation of the (2 + 1)-dimensional Nizhnik–Novikov–Veselov equation. As a result, single soliton solution, single soliton-like solution, multi-soliton solution, multi-soliton-like solution, the rational solution and other exact solutions of the (2 + 1)-dimensional Nizhnik–Novikov–Veselov equation are found. These solutions may be useful to explain some physical phenomena.

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