Integration of the negative order Korteweg-de Vries equation by the inverse scattering method
G. U. Urazboev, Iroda Ismailovna Baltaeva, O. B. Ismoilov
2023Vestnik Udmurtskogo Universiteta Matematika Mekhanika Komp yuternye Nauki10 citationsDOIOpen Access PDF
Abstract
In this paper, we consider the integration of the negative order Korteweg-de Vries equation by the inverse scattering method. The evolution of the spectral data of the Sturm-Liouville operator with a potential associated with the solution of the negative order Korteweg-de Vries equation is determined. The obtained results make it possible to apply the method of inverse scattering problem to solve the negative order Korteweg-de Vries equation in the class of rapidly decreasing functions.
Topics & Concepts
Korteweg–de Vries equationInverse scattering transformInverse scattering problemMathematicsInverseInverse problemMathematical analysisOrder (exchange)ScatteringOperator (biology)Mathematical physicsQuantum inverse scattering methodDispersionless equationApplied mathematicsPhysicsDifferential equationKadomtsev–Petviashvili equationCharacteristic equationChemistryNonlinear systemQuantum mechanicsEconomicsGeneRepressorGeometryFinanceTranscription factorBiochemistryNonlinear Waves and SolitonsAdvanced Mathematical Physics ProblemsOptical properties and cooling technologies in crystalline materials