Note On Eisenstein’s System of Differential Equations: An Example of “Exactly Solvable But Not Completely Integrable System of Differential Equations”

2018 ◽  
pp. 99-115
Author(s):  
David V. Chudnovsky
Keyword(s):  
Differential Equations ◽  
Integrable System ◽  
System Of Differential Equations ◽  
Completely Integrable ◽  
Completely Integrable System ◽  
Exactly Solvable

Soliton Connection of the sinh-Gordon Equation

1984 ◽  
Vol 39 (9) ◽  
pp. 917-918 ◽  
Author(s):  
A. Grauel
Keyword(s):  
Differential Equations ◽  
Lie Algebra ◽  
Integrable System ◽  
Gordon Equation ◽  
Nonlinear Differential Equations ◽  
Differential Forms ◽  
Completely Integrable ◽  
Completely Integrable System ◽  
Derivatives Of

It is demonstrated that the sinh-Gordon equation can be written as covariant exterior derivatives of Lie algebra valued differential forms and, moreover, that these nonlinear differential equations represent a completely integrable system.

scholarly journals SINGULAR COTANGENT MODEL

2014 ◽  
Vol 57 (2) ◽  
pp. 415-430
Author(s):  
CARLOS CURRÁS-BOSCH
Keyword(s):  
Integrable System ◽  
Cotangent Bundle ◽  
Affine Structure ◽  
Completely Integrable ◽  
Completely Integrable System

AbstractAny singular level of a completely integrable system (c.i.s.) with non-degenerate singularities has a singular affine structure. We shall show how to construct a simple c.i.s. around the level, having the above affine structure. The cotangent bundle of the desingularized level is used to perform the construction, and the c.i.s. obtained looks like the simplest one associated to the affine structure. This method of construction is used to provide several examples of c.i.s. with different kinds of non-degenerate singularities.

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