Integrable coupling system of fractional soliton equation hierarchy

2009 ◽  
Vol 373 (41) ◽  
pp. 3730-3733 ◽  
Author(s):  
Fajun Yu
Keyword(s):  
Soliton Equation ◽  
Coupling System ◽  
Integrable Coupling

scholarly journals A Hierarchy of Discrete Integrable Coupling System with Self-Consistent Sources

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yuqing Li ◽  
Huanhe Dong ◽  
Baoshu Yin
Keyword(s):  
Quadratic Form ◽  
Hamiltonian Structure ◽  
Liouville Integrability ◽  
Soliton Equation ◽  
Coupling System ◽  
Self Consistent ◽  
Integrable Coupling

Integrable coupling system of a lattice soliton equation hierarchy is deduced. The Hamiltonian structure of the integrable coupling is constructed by using the discrete quadratic-form identity. The Liouville integrability of the integrable coupling is demonstrated. Finally, the discrete integrable coupling system with self-consistent sources is deduced.

ADJOINT SYMMETRY CONSTRAINTS AND INTEGRABLE COUPLING SYSTEM OF MULTICOMPONENT KN EQUATIONS

2011 ◽  
Vol 25 (21) ◽  
pp. 2841-2852 ◽  
Author(s):  
FA-JUN YU
Keyword(s):  
Spectral Problem ◽  
Arbitrary Order ◽  
Hamiltonian Formulation ◽  
Soliton Equation ◽  
Order Matrix ◽  
Coupling System ◽  
Soliton Hierarchy ◽  
Symmetry Constraints ◽  
Matrix Spectral Problem ◽  
Integrable Coupling

A soliton hierarchy of multicomponent KN equations is generated from an arbitrary order matrix spectral problem, along with its bi-Hamiltonian formulation. Adjoint symmetry constraints are presented to manipulate binary nonlinearization for the associated arbitrary order matrix spectral problem. Finally, a class of integrable coupling systems of the multicomponent KN soliton equation hierarchy is obtained using Ma's method associated with enlarging spectral problems [W. X. Ma, Phys. Lett. A316, 72–76 (2003)].

scholarly journals A Complex Integrable Hierarchy and Its Hamiltonian Structure for Integrable Couplings of WKI Soliton Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fajun Yu ◽  
Shuo Feng ◽  
Yanyu Zhao
Keyword(s):  
Hamiltonian Structure ◽  
Direct Application ◽  
Integrable Hierarchy ◽  
Soliton Equation ◽  
Zero Curvature ◽  
Coupling System ◽  
Soliton Hierarchy ◽  
Integrable Couplings ◽  
Nonlinear Composite ◽  
Integrable Coupling

We generate complex integrable couplings from zero curvature equations associated with matrix spectral problems in this paper. A direct application to the WKI spectral problem leads to a novel soliton equation hierarchy of integrable coupling system; then we consider the Hamiltonian structure of the integrable coupling system. We select theU¯,V¯and generate the nonlinear composite parts, which generate new extended WKI integrable couplings. It is also indicated that the method of block matrix is an efficient and straightforward way to construct the integrable coupling system.

A SIMPLE METHOD TO CONSTRUCT INTEGRABLE COUPLING SYSTEM FOR THE MKdV EQUATION HIERARCHY

2009 ◽  
Vol 23 (02) ◽  
pp. 171-182
Author(s):  
FAJUN YU
Keyword(s):  
Kronecker Product ◽  
Mkdv Equation ◽  
Direct Application ◽  
Soliton Equation ◽  
Simple Method ◽  
Nilpotent Matrix ◽  
Straightforward Method ◽  
Coupling System ◽  
Integrable Couplings ◽  
Integrable Coupling

In this paper, we will extend Ma's method to construct the integrable couplings of soliton equation hierarchy with the Kronecker product and two-nilpotent matrix. A direct application to the MKdV spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is shown that the study of integrable couplings using the Kronecker product is an efficient and straightforward method.

A KIND OF NEW CONTINUOUS LIMITS OF AN INTEGRABLE COUPLING SYSTEM FOR DISCRETE AKNS HIERARCHY

2011 ◽  
Vol 25 (26) ◽  
pp. 3443-3454
Author(s):  
FA-JUN YU
Keyword(s):  
Spectral Problem ◽  
Lie Algebra ◽  
Continuous Limit ◽  
Soliton Equation ◽  
Akns Hierarchy ◽  
Complex Lattice ◽  
Coupling System ◽  
Integrable Couplings ◽  
Integrable Coupling

We present a kind of new continuous limits of an integrable coupling system for discrete AKNS hierarchy by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, a coupling lattice hierarchy is derived. It is shown that a new sequence of combinations of complex lattice spectral problem converges to the integrable couplings of soliton equation hierarchy, which has the integrable coupling system of AKNS hierarchy as a continuous limit.

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