Darboux transformations, covariance theorems and integrable systems

2000 ◽  
pp. 179-209 ◽  
Author(s):  
V. B. Matveev
Keyword(s):  
Integrable Systems ◽  
Darboux Transformations

scholarly journals Darboux transformations with tetrahedral reduction group and related integrable systems

2016 ◽  
Vol 57 (9) ◽  
pp. 092701 ◽  
Author(s):  
George Berkeley ◽  
Alexander V. Mikhailov ◽  
Pavlos Xenitidis
Keyword(s):  
Integrable Systems ◽  
Darboux Transformations ◽  
Reduction Group

TWO ENLARGED LOOP ALGEBRAS FOR OBTAINING NEW INTEGRABLE HIERARCHIES

2011 ◽  
Vol 25 (19) ◽  
pp. 2637-2656
Author(s):  
YUFENG ZHANG ◽  
HONWAH TAM ◽  
WEI JIANG
Keyword(s):  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Soliton Solutions ◽  
Loop Algebra ◽  
Darboux Transformations ◽  
Soliton Equation ◽  
Hamiltonian Structures ◽  
Soliton Theory ◽  
Loop Algebras ◽  
Soliton Hierarchy

Taking a loop algebra [Formula: see text] we obtain an integrable soliton hierarchy which is similar to the well-known Kaup–Newell (KN) hierarchy, but it is not. We call it a modified KN (mKN) hierarchy. Then two new enlarged loop algebras of the loop algebra [Formula: see text] are established, respectively, which are used to establish isospectral problems. Thus, two various types of integrable soliton-equation hierarchies along with multi-component potential functions are obtained. Their Hamiltonian structures are also obtained by the variational identity. The second hierarchy is integrable couplings of the mKN hierarchy. This paper provides a clue for generating loop algebras, specially, gives an approach for producing new integrable systems. If we obtain a new soliton hierarchy, we could deduce its symmetries, conserved laws, Darboux transformations, soliton solutions and so on. Hence, the way presented in the paper is an important aspect to obtain new integrable systems in soliton theory.

scholarly journals Differential Galois theory and Darboux transformations for Integrable Systems

2017 ◽  
Vol 115 ◽  
pp. 75-88
Author(s):  
Sonia Jiménez ◽  
Juan J. Morales-Ruiz ◽  
Raquel Sánchez-Cauce ◽  
María-Angeles Zurro
Keyword(s):  
Integrable Systems ◽  
Galois Theory ◽  
Differential Galois Theory ◽  
Darboux Transformations
Sign in / Sign up

Export Citation Format

Share Document