Article

On exact finite-gap solutions of the negative-order Korteweg–de Vries equation

G. U. UrazboevKhorezm Branch of the Romanovsky Institute of Mathematics, Uzbekistan Academy of Sciences, Urgench, UzbekistanM. M. KhasanovUrgench State University, Urgench, Uzbekistan

Theoretical and Mathematical Physicsjournal2026en

ABI

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.

Topics

Nonlinear Waves and Solitons Quantum Mechanics and Non-Hermitian Physics Spectral Theory in Mathematical Physics

Identifiers

DOI: 10.1134/s0040577926010058

Citations and references

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