arXiv subjects
Publications and source records attributed to Sasanka Ghosh.
The novel inelastic collision properties of two-soliton interaction for an $n$-component coupled higher order nonlinear Schrödinger equation are studied. Some interesting features of three soliton interactions, related to the integrability of the $n$-component coupled higher order nonlinear Schrödinger equation are also discussed.
The N=2 supersymmetric KdV equation of Inami and Kanno is bilinearized employing the Hirota method and the existence of $N$ soliton solutions is demonstrated. The exact form of the solutions are explicitly obtained and an interesting symmetry of the equations of motion is observed.
Two different types of N=1 modified KdV equations are shown to possess $N$ soliton solutions. The soliton solutions of these equations are obtained by casting the equations in the bilinear forms using the supersymmetric extension of the Hirota method. The distinguishing features of the soliton solutions of N=1 mKdV and N=1 mKdV B equations are discussed.
We show that the supersymmetric KdV and KP equations, related to the non-trivial flows, can be cast in the Hirota bilinear form. The existence of one, two and subsequently $N$-soliton solutions is explicitly demonstrated.
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.
Existence of a new class of soliton solutions is shown for higher order nonlinear Schrodinger equation, describing thrid order dispersion, Kerr effect and stimulated Raman scattering. These new solutions have been obtaiened by invoking a group of nonlinear transformations acting on localised stable solutions. Stability of these solutions has been studied for different values of the arbitrary coefficients, involved in the recursion relation and consequently, different values of coefficient lead to different transmission rates for almost same input power. Another series solution containing even powers of localised stable solution is shown to exist for 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.
We show the complete integrability and the existence of optical solitons of higher order nonlinear Schrodinger equation by inverse scattering method for a wide range of values of coefficients. This is achieved first by invoking a novel connection between the integrability of a nonlinear evolution equation and the dimensions of a family of matrix Lax pairs. It is shown that Lax pairs of different dimensions lead to the same evolution equation only with the coefficients of the terms in different integer ratios. Optical solitons, thus obtained by inverse scattering method, have been found by solving an n dimensional eigenvalue problem.
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 o
We look for a graviton-dilaton theory which can predict non trivial values of the PPN parameters $β$ and/or $γ$ for a charge neutral point star, without any naked singularity. With the potential for dilaton $ϕ$ set to zero, it contains one arbitrary function $ψ(ϕ)$. Our requirements impose certain constraints on $ψ$, which lead to the following generic and model independent novel results: For a charge neutral point star, the gravitational force becomes repulsive at distances of the order of, but greater than, the Schwarzschild radius $r_0$. There is also no horizon for $r > r_0$. These results suggest that black holes are unlikely to form in a stellar collapse in this theory.
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.
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.
It is shown that $SL(n,R)$ KdV hierarchy can be expressed as definite nonpolynomials in Kac Moody currents and their derivatives by the action of Borel subgroup of $SL(n,R)$ on the phase space of centrally extended $sl(n,R)$ Kac Moody currents. Construction of Lax pair is shown, confirming Drinfeld Sokolov type Hamiltonian reduction. This suggests an example of a moduli space with symplectic structure corresponding to extended conformal symmetries.