A new approach to the Boussinesq hierarchy

Mie develop a new systematic approach to the Boussinesq (Bsq) hierarchy based on elementary algebraic methods. In particular, we recursively construct Lax pairs for the Bsq hierarchy by introducing a Fundamental polynomial formalism and establish the basic algebro -- geometric setting including associated Burchnall-Chaundy curves, Baker-Akhiezer functions, trace formulas, and Dubrovin-type equations for Dirichlet and Neumann divisors.