Stability Conditions for Solutions of Multidimensional Completely Integrable Differential Equations

2018 ◽  
Vol 54 (8) ◽  
pp. 1026-1031
Author(s):  
L. B. Knyazhishche
Keyword(s):  
Differential Equations ◽  
Stability Conditions ◽  
Completely Integrable

scholarly journals New Neumann System Associated with a 3 × 3 Matrix Spectral Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Fang Li ◽  
Liping Lu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Spectral Problem ◽  
Hamiltonian Systems ◽  
Lax Pair ◽  
Completely Integrable ◽  
Neumann System ◽  
Matrix Spectral Problem

The nonlinearization approach of Lax pair is applied to the case of the Neumann constraint associated with a 3 × 3 matrix spectral problem, from which a new Neumann system is deduced and proved to be completely integrable in the Liouville sense. As an application, solutions of the first nontrivial equation related to the 3 × 3 matrix spectral problem are decomposed into solving two compatible Hamiltonian systems of ordinary differential equations.

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.

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