Conformai invariant Painlevé expansions and higher dimensional integrable models

1999 ◽  
Vol 42 (5) ◽  
pp. 537-545 ◽  
Author(s):  
Senyue Lou
Keyword(s):  
Integrable Models ◽  
Higher Dimensional

Higher Dimensional Integrable Models with Painleve Property Obtained from (1+1)-Dimensional Schwarz KdV Equation

1998 ◽  
Vol 53 (8) ◽  
pp. 689-692 ◽  
Author(s):  
Li-li Chen ◽  
Sen-yue Loua
Keyword(s):  
Kdv Equation ◽  
Integrable Models ◽  
Painlevé Analysis ◽  
Higher Dimensional ◽  
Painlevé Property ◽  
Painleve Analysis

Abstract Using the extended Painlevé analysis, we obtained some higher dimensional integrable models with the Painlevé property from the (1+1)-dimensional Schwarz KdV equation.

scholarly journals Higher Dimensional Integrable Models from Lower Ones via Miura Type Deformation Relation

2000 ◽  
Vol 55 (11-12) ◽  
pp. 867-876 ◽  
Author(s):  
Sen-yue Lou ◽  
Jun Yu ◽  
Xiao-yan Tang
Keyword(s):  
Heat Conduction ◽  
Exact Solutions ◽  
Heat Conduction Equation ◽  
Soliton Solutions ◽  
Integrable Models ◽  
High Dimensional ◽  
Systematic Method ◽  
Type Transformation ◽  
Higher Dimensional ◽  
Physical Fields

Abstract To find nontrivial high dimensional integrable models (especially in (3+1)-dimensions) is one of the most important problems in nonlinear physics. A systematic method to find some nontrivial high dimensional integrable models is established by means of noninvertible deformation relations. Starting from a noninvertible Miura type transformation, we find that the (1+1)-dimensional sinh-Gordon model appearing in many physical fields is a deformation of the (0+1)-dimensional Riccati equation. A high dimensional Miura type deformation (including two different (3+1)-dimensional reductions) of the heat conduction equation is proved to be Painlevé integrable. Some special types of explicit exact solutions, like multi-plane and/or multi-camber soliton solutions, multi-dromion solutions and multiple ring soliton solutions, are obtained.

scholarly journals INTEGRABLE MODELS AND THE HIGHER DIMENSIONAL REPRESENTATIONS OF GRADED LIE ALGEBRAS

1998 ◽  
Vol 13 (02) ◽  
pp. 133-144
Author(s):  
J. C. BRUNELLI ◽  
ASHOK DAS
Keyword(s):  
Lie Algebras ◽  
Integrable Models ◽  
Fundamental Representation ◽  
Graded Lie Algebras ◽  
Systematic Method ◽  
Curvature Condition ◽  
Zero Curvature ◽  
Higher Dimensional

We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis, further, suggests a systematic method of constructing higher dimensional representations for the zero curvature condition starting with the fundamental representation. We illustrate this with the examples of the sTB hierarchy and the sKdV hierarchy. This would be particularly useful in constructing explicit higher dimensional representations of graded Lie algebras.

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