Asymptotic benaviour of the resolvent of Sturm–Liouville equations and the algebra of the Korteweg–de Vries equations

This paper is concerned with a group of problems associated with recent results on non-linear equations of Korteweg-de Vries type. The second chapter is basically of a survey character and investigates connections between these equations and trace formulae. In the first chapter we develop a new algebraic formalism of the calculus of variations.