Mc'Kean's transformation for 3-rd order operators

2024/06/14 by Andrey Badanin, Badanin, Andrey, Evgeny Korotyaev +1
Computer Science · #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2406.09668

Abstract

We consider a non-self-adjoint third order operator (y''+py)'+py'+qy with 1-periodic coefficients p,q. This operator is the L-operator in the Lax pair for the good Boussinesq equation on the circle. In 1981, McKean introduced a transformation that reduces the spectral problem for this operator to a spectral problem for the Hill operator with a potential that depends analytically on the energy. In the present paper we are studying this transformation.

Related

• Inverse problem for the L-operator in the Lax Pair of the Boussinesq equation on the circle
• Third order operators with three-point conditions associated with Boussinesq's equation
• Inverse problem for 3-rd order operators under the 3-point Dirichlet conditions
• Third order operator with periodic coefficients on the real line
• Asymptotics of the divisor for the good Boussinesq equation