32 research outputs found
Integrability and Symmetry Algebra Associated with N=2 KP Flows
We show the complete integrability of N=2 nonstandard KP flows establishing
the biHamiltonian structures. One of Hamiltonian structures is shown to be
isomorphic to the nonlinear N=2 algebra with the bosonic
sector having structure. A consistent
free field representation of the super conformal algebra is obtained. The
bosonic generators are found to be an admixture of free fermions and free
complex bosons, unlike the linear one. The fermionic generators become
exponential in free fields, in general.Comment: Latex file, 38 pages, no figure
N = 2 Super Algebra and its Nonlinear Realization Through Super KP Formulation
A nonlinear realization of super algebra is shown to exist
through a consistent superLax formulation of super KP hierarchy. The reduction
of the superLax operator gives rise to the Lax operators for generalized
super KdV hierarchies, proposed by Inami and Kanno. The Lax equations are shown
to be Hamiltonian and the associated Poisson bracket algebra among the
superfields, consequently, gives rise to a realization of nonlinear super
algebra.Comment: 13, MRI-PHY 7/94 SNBC 06/9
Interaction of Coupled Higher Order Nonlinear SCHR\"Odinger Equation Solitons
The novel inelastic collision properties of two-soliton interaction for an
-component coupled higher order nonlinear Schr\"odinger equation are
studied. Some interesting features of three soliton interactions, related to
the integrability of the -component coupled higher order nonlinear
Schr\"odinger equation are also discussed.Comment: 6 pages, 4 figures, revtex
Soliton solutions, Liouville integrability and gauge equivalence of Sasa Satsuma equation
Exact integrability of the Sasa Satsuma eqation (SSE) in the Liouville sense
is established by showing the existence of an infinite set of conservation
laws. The explicit form of the conserved quantities in term of the fields are
obtained by solving the Riccati equation for the associated 3x3 Lax operator.
The soliton solutions in particular, one and two soliton solutions, are
constructed by the Hirota's bilinear method. The one soliton solutions is also
compared with that found through the inverse scattering method. The gauge
equivalence of the SSE with a generalized Landau Lifshitz equation is
established with the explicit construction oComment: 14 pages, to be published in J. Math. Phys. April-May, 199
The Hamiltonian Structures of the super KP hierarchy Associated with an Even Parity SuperLax Operator
We consider the even parity superLax operator for the supersymmetric KP
hierarchy of the form and obtain
the two Hamiltonian structures following the standard method of Gelfand and
Dikii. We observe that the first Hamiltonian structure is local and linear
whereas the second Hamiltonian structure is non-local and nonlinear among the
superfields appearing in the Lax operator. We discuss briefly on their
connections with the super algebra.Comment: 14 pages, Plain tex, IC/93/17
Inverse scattering method and vector higher order nonlinear Schrodinger equation
A generalised inverse scattering method has been developed for arbitrary n
dimensional Lax equations. Subsequently, the method has been used to obtain N
soliton solutions of a vector higher order nonlinear Schrodinger equation,
proposed by us. It has been shown that under suitable reduction, vector higher
order nonlinear Schrodinger equation reduces to higher order nonlinear
Schrodinger equation. The infinite number of conserved quantities have been
obtained by solving a set of coupled Riccati equation. A gauge equivalence is
shown between the vector higher order nonlinear Schrodinger equation and the
generalized Landau Lifshitz equation and the Lax pair for the latter equation
has also been constructed in terms of the spin field, establishing direct
integrability of the spin system.Comment: 28 page