A New Approach to the Boussinesq Hierarchy

Abstract

Abstract We 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.