Bilinearization of nonlinear integrable evolution equations: Recursion operator approach

2021 ◽  
pp. 305-324
Author(s):  
Xing-Biao Hu ◽  
Guo-Fu Yu
Keyword(s):  
Evolution Equations ◽  
Recursion Operator ◽  
Operator Approach ◽  
Integrable Evolution

A HIERARCHY OF HAMILTONIAN EQUATIONS ASSOCIATED WITH THE MODIFIED JAULENT–MIODEK HIERARCHY

2010 ◽  
Vol 24 (02) ◽  
pp. 183-193
Author(s):  
HAI-YONG DING ◽  
HONG-XIANG YANG ◽  
YE-PENG SUN ◽  
LI-LI ZHU
Keyword(s):  
Eigenvalue Problem ◽  
Evolution Equations ◽  
Trace Identity ◽  
Liouville Integrability ◽  
Matrix Eigenvalue Problem ◽  
Hamiltonian Structures ◽  
Hamiltonian Equations ◽  
Matrix Eigenvalue ◽  
Integrable Evolution

By considering a new four-by-four matrix eigenvalue problem, a hierarchy of Lax integrable evolution equations with four potentials is derived. The Hamiltonian structures of the resulting hierarchy are established by means of the generalized trace identity. The Liouville integrability for the hierarchy of the resulting Hamiltonian equations is presented.

A FOUR-BY-FOUR MATRIX EIGENVALUE PROBLEM, RELATED HIERARCHY OF LAX INTEGRABLE EQUATIONS AND THEIR HAMILTONIAN STRUCTURES

2008 ◽  
Vol 22 (23) ◽  
pp. 4027-4040 ◽  
Author(s):  
XI-XIANG XU ◽  
HONG-XIANG YANG ◽  
WEI-LI CAO
Keyword(s):  
Eigenvalue Problem ◽  
Evolution Equations ◽  
Trace Identity ◽  
Liouville Integrability ◽  
Matrix Eigenvalue Problem ◽  
Hamiltonian Structures ◽  
Hamiltonian Equations ◽  
Integrable Equations ◽  
Matrix Eigenvalue ◽  
Integrable Evolution

Starting from a new four-by-four matrix eigenvalue problem, a hierarchy of Lax integrable evolution equations with four potentials is derived. The Hamiltonian structures of the resulting hierarchy are established by means of the generalized trace identity. The Liouville integrability for the hierarchy of the resulting Hamiltonian equations is proved.

Sign in / Sign up

Export Citation Format

Share Document