Prasad started his career as a lecturer in the Department of Applied Mathematics in 1967 at Indian Institute of Science, thereafter he became a Professor in 1977. Meanwhile, he also remained a Postdoctoral Fellow at Leeds University (1970–72) and Alexander von Humboldt Fellow (1980-81).[1] He was at the St John's College, Cambridge with privileges of a Fellow of the College. At IISc, he held Distinguished chair of MSIL Professorship during 1993-96, was Chairman of the Department of Mathematics during 1996-2000, was Professor in super-time-scale before his retirement on 31 July, 2006, was Honorary Professor during 2006-2011, was DAE Raja Ramanna Fellow also during 2006-2011, was INSA Senior Scientist in 2011, was NASI-Senior Scientist Platinum Jubilee Fellow during 2012 -2016
Prasad has done some significant work in the area on non-linear hyperbolic equations. He succeeded in assessing the basic properties of the equations of various physical phenomena, generalized these mathematical properties and then used his theory to explain new results in the field of non-linear waves. He gave a proof of the existence of a new type of wave on the interface of a clear liquid and a mixture in a sedimentation process.[2]
