Related papers: A three-by-three matrix spectral problem for AKNS …
A kind of Bargmann symmetry constraints involving Lax pairs and adjoint Lax pairs is proposed for soliton hierarchy. The Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative finite dimensional integrable…
Binary nonlinearization of AKNS spectral problem is extended to the cases of higher-order symmetry constraints. The Hamiltonian structures, Lax representations, $r$-matrices and integrals of motion in involution are explicitly proposed for…
Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax…
This paper aims to show that there exist non-symmetry constraints which yield integrable Hamiltonian systems through nonlinearization of spectral problems of soliton systems, like symmetry constraints. Taking the AKNS spectral problem as an…
A Bargmann symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the Dirac systems. It is shown that the spatial part of the nonlinearized Lax pairs and adjoint Lax pairs is a finite dimensional Liouville integrable…
Binary Bargmann symmetry constraints are applied to decompose soliton equations into finite-dimensional Liouville integrable Hamiltonian systems, generated from so-called constrained flows. The resulting constraints on the potentials of…
We propose a scheme for nonlinearizing linear equations to generate integrable nonlinear systems of both the AKNS and the KN classes, based on the simple idea of dimensional analysis and detecting the building blocks of the Lax pair. Along…
We establish the binary nonlinearization approach of the spectral problem of the super AKNS system, and then use it to obtain the super finite-dimensional integrable Hamiltonian system in supersymmetry manifold $\mathbb{R}^{4N|2N}$. The…
A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for…
It is shown that the Zakharov-Mihailov (ZM) Lagrangian structure for integrable nonlinear equations derived from a general class of Lax pairs possesses a Lagrangian multiform structure. We show that, as a consequence of this multiform…
The method of nonlinearization of the Lax pair is developed for the Ablowitz-Kaup-Newell-Segur (AKNS) equation in the presence of space-inverse reductions. As a result, we obtain a new type of finite-dimensional Hamiltonian systems: they…
We study, systematically, the properties of the supersymmetric AKNS (sAKNS) hierarchy. In particular, we discuss the Lax representation in terms of a bosonic Lax operator and some special features of the equations and construct the bosonic…
A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure.…
It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator.We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a…
We present a method for constructing hierarchies of solutions to $n$-simplex equations by variating the spectral parameter in their Lax representation. We use this method to derive new solutions to the set-theoretical 2- and 3-simplex…
We present multiplicity results for the periodic and Neumann-type boundary value problems associated with coupled Hamiltonian systems. For the periodic problem, we couple a system having twist condition with another one whose nonlinearity…
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is…
We consider an integrable generalization of the nonlinear Schr\"odinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS equation in the same way that the…
We obtain via B\"acklund transformation the Hamiltonian representation for a Lax type nonlinear dynamical system hierarchy on a dual space to the Lie algebra of super-integral-differential operators of one anticommuting variable, extended…
In this paper, a new generalized $5\times5$ matrix spectral problem of Ablowitz-Kaup-Newell-Segur(AKNS) type associated with the enlarged matrix Lie super algebra is proposed and its corresponding super soliton hierarchy is established. The…