Biomedical subjects

Avinash Khare

Publications and source records attributed to Avinash Khare.

6 recordsLinked to original sources

PubMed2006

Discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities.

A class of discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrödinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.

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PubMed2005

Exact solitary wave solutions for a discrete lambdaphi4 field theory in 1+1 dimensions.

We have found exact, periodic, time-dependent solitary wave solutions of a discrete phi4 field theory model. For finite lattices, depending on whether one is considering a repulsive or attractive case, the solutions are Jacobi elliptic functions, either sn (x,m) [which reduce to the kink function tanh (x) for m-->1 ], or they are dn (x,m) and cn (x,m) [which reduce to the pulse function sech (x) for m-->1 ]. We have studied the stability of these solutions numerically, and we find that our solutions are linearly stable in most cases. We show that this model is a Hamiltonian system, and that the effective Peierls-Nabarro barrier due to discreteness is zero not only for the two localized modes but even for all three periodic solutions. We also present results of numerical simulations of scattering of kink-antikink and pulse-antipulse solitary wave solutions.

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PubMed2004

Solitary wave interactions in dispersive equations using Manton's approach.

We generalize the approach first proposed by Manton [Nucl. Phys. B 150, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations that support such localized solutions. The approach is illustrated using as examples solitons in the Korteweg-de Vries equation, standing waves in the nonlinear Schrödinger equation, and kinks as well as breathers of the sine-Gordon equation.

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PubMed2003

Breather lattice and its stabilization for the modified Korteweg-de Vries equation.

We obtain an exact solution for the breather lattice solution of the modified Korteweg-de Vries equation. Numerical simulation of the breather lattice demonstrates its instability due to the breather-breather interaction. However, such multibreather structures can be stabilized through the concurrent application of ac driving and viscous damping terms.

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PubMed2002

Quantum modes on chaotic motion: Analytically exact results.

We discover a class of chaotic quantum systems for which we obtain some analytically exact eigenfunctions in closed form. These results have been possible due to connections shown between random matrix models, many-body theories, and dynamical systems. We believe that these results and connections will pave the way to a better understanding of quantum chaos.

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PubMed2002

Linear superposition in nonlinear equations.

Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions.

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