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We develop the idea of selectively manipulating the condensate in a trappedBose-condensed gas, without perturbing the thermal cloud. The idea is based onthe possibility to modify the mean field interaction between atoms (scatteringlength) by nearly resonant incident light or by spatially uniform change of thetrapping magnetic field. For the gas in the Thomas-Fermi regime we findanalytical scaling solutions for the condensate wavefunction evolving underarbitrary variations of the scattering length $a$. The change of $a$ frompositive to negative induces a global collapse of the condensate, and the finalstages of the collapse will be governed by intrinsic decay processes.

Evolution and Global Collapse of Trapped Bose Condensates under Variations of the Scattering Length