  The asymmetric simple exclusion process (ASEP) is a paradigmatic integrable
stochastic model describing nonequilibrium transport phenomena. In this paper,
we investigate solutions of the Bethe equations for the ASEP in the
thermodynamic limit. Many hermitian integrable systems, such as the Heisenberg
spin chain, have regular solutions called string solutions. However, in the
case of the ASEP, the pattern of the string solution is changed due to its
non-hermiticity. We call this new type of string solutions "bundled string
solutions". We introduce and formulate the bundled string solutions, and then
derive the extended Bethe-Takahashi equations.
