Non-isospectral Multi-component AKNS Equations and New Integrable Couplings
نویسندگان
چکیده
Positive and negative hierarchies of non-isospectral multi-component AKNS equations are derived from an arbitrary order matrix spectral problem. Moreover, new non-isospectral multi-component integrable couplings of the resulting soliton hierarchies are constructed by enlarging the associated matrix spectral problem. Mathematics Subject Classification: 35Q58
منابع مشابه
The Algebraic Structure of Zero Curvature Representations Associated with Integrable Couplings
The commutator of enlarged vector fields was explicitly computed for integrable coupling systems associated with semidirect sums of Lie algebras. An algebraic structure of zero curvature representations is then established for such integrable coupling systems. As an application example of this algebraic structure, the commutation relations of Lax operators corresponding to the enlarged isospect...
متن کاملNonlinear bi-integrable couplings with Hamiltonian structures
Bi-integrable couplings of soliton equations are presented through introducing non-semisimple matrix Lie algebras on which there exist non-degenerate, symmetric and ad-invariant bilinear forms. The corresponding variational identity yields Hamiltonian structures of the resulting bi-integrable couplings. An application to the AKNS spectral problem gives bi-integrable couplings with Hamiltonian s...
متن کاملLoop Algebras and Bi-integrable Couplings∗
A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations. The variational identities under non-degenerate, symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings. A special case of the s...
متن کاملIntegrable Couplings, Variational Identities and Hamiltonian Formulations
We discuss Hamiltonian formulations for integrable couplings, particularly biand tri-integrable couplings, based on zero curvature equations. The basic tools are the variational identities over non-semisimple Lie algebras consisting of block matrices. Illustrative examples include dark equations and biand tri-integrable couplings of the KdV equation and the AKNS equations, generated from the en...
متن کاملDarboux Transformation for the Non-isospectral AKNS Hierarchy and Its Asymptotic Property
In this article, the Darboux transformation for the non-isospectral AKNS hierarchy is constructed. We show that the Darboux transformation for the non-isospectral AKNS hierarchy is not an auto-Bäcklund transformation, because the integral constants of the hierarchy will be changed after the transformation. The transform rule of the integral constants will be also derived. By this means, the sol...
متن کامل