Integrability and Exact Solutions of Complexly Coupled Kdv System: PainlevÉ Property and Bäcklund Transformation

2012 ◽  
Vol 2 (2) ◽  
pp. 14-16
Author(s):  
G. M. Moatimid ◽  
M. H. M. Moussa ◽  
Rehab M. El-Shiekh ◽  
A. A. El-Satar
Keyword(s):  
Exact Solutions ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Painlevé Property

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.

EXACT SOLUTIONS AND COMPLEX WAVE EXCITATIONS OF GENERALIZED SASA–SATSUMA SYSTEM IN (2+1)-DIMENSIONS

2009 ◽  
Vol 23 (19) ◽  
pp. 3931-3938 ◽  
Author(s):  
CHUN-LONG ZHENG ◽  
JIAN-FENG YE
Keyword(s):  
Exact Solutions ◽  
Solitary Waves ◽  
Bäcklund Transformation ◽  
Periodic Wave ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Complex Wave

Starting from a Painlevé–Bäcklund transformation, an exact variable separation solution with four arbitrary functions for the (2+1)-dimensional generalized Sasa–Satsuma (GSS) system are derived. Based on the derived exact solutions in the paper, some complex wave excitations in the (2+1)-dimensional GSS system and revealed, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave background are also briefly discussed.

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.

A note on the exact solutions for non-conservative three-wave resonance

1987 ◽  
Vol 106 (3-4) ◽  
pp. 205-207 ◽  
Author(s):  
A. D. D. Craik
Keyword(s):  
Exact Solutions ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Lump Solutions ◽  
Wave Resonance ◽  
The One

SynopsisExact solutions recently discovered for non-conservative three-wave resonance are here related to the ‘one-lump’ solutions obtained by Backlund transformation in conservative cases.

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