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 $\hat W_{\infty}$ algebra with the bosonic sector having $\hat W_{1+\infty}\oplus \hat W_{\infty}$ 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 W∞W_{\infty} Algebra and its Nonlinear Realization Through Super KP Formulation

A nonlinear realization of super $W_{\infty}$ 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 $N=2$ 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 $W_{\infty}$ algebra.Comment: 13, MRI-PHY 7/94 SNBC 06/9

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

Interaction of Coupled Higher Order Nonlinear SCHR\"Odinger Equation Solitons

The novel inelastic collision properties of two-soliton interaction for an $n$-component coupled higher order nonlinear Schr\"odinger equation are studied. Some interesting features of three soliton interactions, related to the integrability of the $n$-component coupled higher order nonlinear Schr\"odinger equation are also discussed.Comment: 6 pages, 4 figures, revtex

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 $L~=~D^2 + \sum_{i=0}^\infty u_{i-2} D^{-i+1}$ 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 $w_{\infty}$ 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