The construction of invariants up to fourth order in velocities has been carried out for one-dimensional, time-dependent classical dynamical systems. While the exact results are recovered for the first and second order integrable systems, the results for the third and fourth order invariants are expressed in terms of nonlinearpotential equations. Noticing the separability of the potential in space and time variables these nonlinear equations are reduced to a tractable form. A possible solution for the third order case suggests a new integrable systemV(q, t) ∼t^−4/3q^1/2.

The construction of the second constant of motion of second order for two-dimensional classical systems is carried out in terms ofz=q₁ +iq₂ andq=q₁ −iq₂. As a result a class of Toda-type potentials admitting second order invariants is explored.

The ground state of a class of potentials described byV(x)=a₂₀x²+a₁/x² is investigated. This potential possesses some distinct features like that of a symmetric double-well potential, and can be used in modelling the fusion process of two identical nuclei as well.

A new system of time-dependent anharmonic and anisotropic oscillators in two space-dimensions which corresponds to unequal but related spring constants, having Hamiltonian structure, admitting quadratic invariants and accounting also for the fractional powers in the coupling terms, is found.

With a view to understand the available data on the momentum- and energy-dependences of theJ/Ψ suppression, we compute the suppression rate within the framework of a hydrodynamical evolution model for the quark-gluon plasma (QGP) formation. We make use of an ansatz for the temperature profile function which accounts not only for the space and time evolutions of QGP but also for the possibility of a mixed phase in the boundary region of the deconfined phase. While the predictions are made for the longitudinal momentum- and energy-dependences of the suppression rate, a satisfactory agreement with the available data is found for its dependences on the transverse momentum and the transverse energy.

Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys.38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding Hamiltonian non-Hermitian.