Self-Consistent Sources and Conservation Laws for a Super Broer-Kaup-Kupershmidt Equation Hierarchy

Based on the matrix Lie superalgebras and supertrace identity, the integrable super Broer-Kaup-Kupershmidt hierarchy with self-consistent sources is established. Furthermore, we establish the infinitely many conservation laws for the integrable super Broer-Kaup-Kupershmidt hierarchy. In the process of computation especially, Fermi variables also play an important role in super integrable systems

A generalized fractional KN equation hierarchy and its fractional Hamiltonian structure

AbstractA generalized Hamiltonian structure of the fractional soliton equation hierarchy is presented by using differential forms and exterior derivatives of fractional orders. We construct the generalized fractional trace identity through the Riemann–Liouville fractional derivative. An example of the fractional KN soliton equation hierarchy and Hamiltonian structure is presented, which is a new integrable hierarchy and possesses Hamiltonian structure

Self-Consistent Sources and Conservation Laws for a Super Broer-Kaup-Kupershmidt Equation Hierarchy

Based on the matrix Lie superalgebras and supertrace identity, the integrable super Broer-Kaup-Kupershmidt hierarchy with self-consistent sources is established. Furthermore, we establish the infinitely many conservation laws for the integrable super Broer-Kaup-Kupershmidt hierarchy. In the process of computation especially, Fermi variables also play an important role in super integrable systems

Super-Hamiltonian Structures and Conservation Laws of a New Six-Component Super-Ablowitz-Kaup-Newell-Segur Hierarchy

A six-component super-Ablowitz-Kaup-Newell-Segur (-AKNS) hierarchy is proposed by the zero curvature equation associated with Lie superalgebras. Supertrace identity is used to furnish the super-Hamiltonian structures for the resulting nonlinear superintegrable hierarchy. Furthermore, we derive the infinite conservation laws of the first two nonlinear super-AKNS equations in the hierarchy by utilizing spectral parameter expansions. PACS: 02.30.Ik; 02.30.Jr; 02.20.Sv

Structure of the conservation laws in integrable spin chains with short range interactions

We present a detailed analysis of the structure of the conservation laws in quantum integrable chains of the XYZ-type and in the Hubbard model. With the use of the boost operator, we establish the general form of the XYZ conserved charges in terms of simple polynomials in spin variables and derive recursion relations for the relative coefficients of these polynomials. For two submodels of the XYZ chain - namely the XXX and XY cases, all the charges can be calculated in closed form. For the XXX case, a simple description of conserved charges is found in terms of a Catalan tree. This construction is generalized for the su(M) invariant integrable chain. We also indicate that a quantum recursive (ladder) operator can be traced back to the presence of a hamiltonian mastersymmetry of degree one in the classical continuous version of the model. We show that in the quantum continuous limits of the XYZ model, the ladder property of the boost operator disappears. For the Hubbard model we demonstrate the non-existence of a ladder operator. Nevertheless, the general structure of the conserved charges is indicated, and the expression for the terms linear in the model's free parameter for all charges is derived in closed form.Comment: 79 pages in plain TeX plus 4 uuencoded figures; (uses harvmac and epsf

A Integrable Generalized Super-NLS-mKdV Hierarchy, Its Self-Consistent Sources, and Conservation Laws

A generalized super-NLS-mKdV hierarchy is proposed related to Lie superalgebra B(0,1); the resulting supersoliton hierarchy is put into super bi-Hamiltonian form with the aid of supertrace identity. Then, the super-NLS-mKdV hierarchy with self-consistent sources is set up. Finally, the infinitely many conservation laws of integrable super-NLS-mKdV hierarchy are presented

The Lax Pair by Dimensional Reduction of Chern-Simons Gauge Theory

We show that the Nonlinear Schr\"odinger Equation and the related Lax pair in 1+1 dimensions can be derived from 2+1 dimensional Chern-Simons Topological Gauge Theory. The spectral parameter, a main object for the Loop algebra structure and the Inverse Spectral Transform, has appear as a homogeneous part (condensate) of the statistical gauge field, connected with the compactified extra space coordinate. In terms of solitons, a natural interpretation for the one-dimensional analog of Chern-Simons Gauss law is given.Comment: 27 pages, Plain Te