  We introduce a new way to study molecular evolution within well-established
Hamilton-Jacobi formalism, showing that for a broad class of fitness landscapes
it is possible to derive dynamics analytically within the $1/N$-accuracy, where
$N$ is genome length. For smooth and monotonic fitness function this approach
gives two dynamical phases: smooth dynamics, and discontinuous dynamics. The
latter phase arises naturally with no explicit singular fitness function,
counter-intuitively. The Hamilton-Jacobi method yields straightforward
analytical results for the models that utilize fitness as a function of Hamming
distance from a reference genome sequence. We also show the way in which this
method gives dynamical phase structure for multi-peak fitness.
