We establish an algebraic structure for zero curvature representations of coupled integrable couplings. The adopted zero curvature representations are associated with Lie algebras possessing two sub-Lie algebras in form of semi-direct sums of Lie algebras. By applying the presented algebraic structures to the AKNS systems, we give an approach for generating τ -symmetry algebras of coupled integ...

Abstract In recent years, new properties of space-time duality in the Hamiltonian formalism certain integrable classical field theories have been discovered and led to their reformulation using ideas from covariant theory: this sense, nature r -matrix structure was unravelled. Here, we solve open question extending these results a whole hierarchy. We choose Ablowitz–Kaup–Newell–Segur (AKNS) To ...

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

We develop a systematic approach to the classical Boussinesq (cBsq) hierarchy based on an elementary polynomial recursion formalism. Moreover, the gauge equivalence between the cBsq and AKNS hierarchies is studied in detail and used to provide an effortless derivation of algebro-geometric solutions and their theta function representations of the cBsq hierarchy .

We study the gauge transformations between the supersymmetric AKNS (sAKNS) and supersymmetric two-boson (sTB) hierarchies. The Hamiltonian nature of these gauge transformations is investigated, which turns out to be canonical. We also obtain the Darboux-Bäcklund transformations for the sAKNS hierarchy from these gauge transformations.

We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.

We consider the eigenvalues of the matrix AKNS system and establish bounds on the location of eigenvalues and criteria for the nonexistence of eigenvalues. We also identify properties of the system which guarantee that eigenvalues cannot lie on the imaginary axis or can only lie on the imaginary axis. Moreover, we study the deficiency indices of the underlying non-selfadjoint differential opera...