On exact finite-gap solutions of the negative-order Korteweg–de Vries equation
Abstract
Abstract We show that the negative-order Korteweg–de Vries equation can be integrated using the inverse spectral problem method. We find the evolution of the spectral data of the Sturm–Liouville operator with a periodic potential associated with the finite-gap solution of the negative-order Korteweg–de Vries equation. The obtained results allow the inverse problem method to be applied to solve the negative-order Korteweg–de Vries equation in the class of periodic functions. We prove important implications regarding the analyticity and the spatial period of the finite-gap solution. We show that the solution constructed by the Dubrovin system of equations and the first trace formula satisfies the negative-order Korteweg–de Vries equation.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Quantum Mechanics and Non-Hermitian Physics
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Theoretical and Mathematical Physics
- Publisher
- Pleiades Publishing Ltd
- Volume
- 226
- Issue
- 1
- Pages
- 87–96
- Publication date
- 1 January 2026
- Language
- EN