This paper is an annotated list of transformation properties and identities satisfied by the four theta functions \(\theta _1\), \(\theta _2\), \(\theta _3\), In this paper, we study the decay rl possible 3, 4 and 5-term identCauchy problem for the one-dimensional viscous conservation law where the far fieldar 3-term identities connecting the theta-functions with modular parameters \(\tau\) and \(2\tau\).