This paper discusses new aspects of the superconducting phenomenology of th
e cuprate high-T-c superconductors in terms of the change in superconductin
g condensation energy and the electronic states in the vortex core due to t
he extreme phenomenological parameters, the d-wave superconducting gap and
the presence of the 'pseudo-gap' in the normal state. It is shown that the
extreme phenomenological parameters and the d-wave superconducting gap make
the vortex state of high-T-c superconductors quite different from that of
conventional superconductors in many aspects both thermodynamically and dyn
amically. Further, we show that the presence of the 'pseudo-gap' should red
uce the condensation energy and increase the penetration depth. The effect
of the 'pseudo-gap' on the vortex pinning is discussed in relation to the e
mpirical scaling laws observed in the phase diagram in the mixed state. (C)
1999 Elsevier Science B.V. All rights reserved.