• Ram K Varma

      Articles written in Pramana – Journal of Physics

    • Korteweg — de Vries solitons with different co-ordinate stretchings

      N Nagesha Rao Ram K Varma

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      The differences between the soliton solutions of the K-dV equation for a homogeneous, collisionless plasma, consisting of cold ions and isothermal electrons arising due to the two different sets of stretched co-ordinates have been discussed. In particular, the differences between the amplitudes and the widths of the solitons and their variations with the soliton velocity have been indicated. Further, the experimental implications of these differences and also of the two sets of stretched co-ordinates have been discussed.

    • Ion acoustic solitary waves in density and temperature gradients

      N Nagesha Rao Ram K Varma

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      The propagation of ion-acoustic K-dV solitary waves in weakly inhomogeneous, collisionless plasmas with gradients both in the density and the temperature of the ions has been considered. The electrons are assumed to be hot and isothermal, and the ions to be warm and adiabatic. The reductive perturbation analysis of the fluid equations is then carried out. The zero order quantities existing in the system due to the presence of the inhomogeneities are taken into account consistently and a set of ‘stretched coordinates’ appropriate for the inhomogeneous system is employed. A more general modified K-dV equation has been derived and its soliton solution is obtained explicitly. It is shown that as the soliton propagates along the temperature gradient, its amplitude and the velocity decrease, and the width increases. Further, it is found that when the two gradients are in opposite directions, the amplitude of the soliton remains constant.

    • Quasi invariants and generalized killing vectors

      B R Sitaram Ram K Varma

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      The connection between quasi-invariants (invariants of a Hamiltonian system defined only on a single constant energy hypersurface) and generalized Killing vector fields associated with the corresponding Jacobi metric is investigated. The results are used to deduce a generalised form of the classical Whittaker problem in two degrees of freedom.

    • Quasi-invariants and generalized Killing vectors-II

      B R Sitaram Ram K Varma

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      We consider here the problem of the existence of a quasi-invariant which is linear in the momenta for Hamiltonians in three degrees of freedom. We show that such quasi-invariants are more constrained in their structure than in the two degrees of freedom case. We also show that some of these quasi-invariants have to be interpreted as ‘pseudo-translations’, i.e., as translations in a non-orthogonal system of coordinates.

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