On Complex-Valued Solutions of the General Loaded Korteweg–de Vries Equation with a Source
А. Б. Хасанов, U. A. Hoitmetov
Abstract
Using the inverse scattering method, we derive the evolution of the scattering data of a nonself-adjoint Sturm–Liouville operator whose potential is a solution of the general loaded Korteweg–de Vries equation with a self-consistent source in the class of rapidly decaying complex-valued functions. An example is given to illustrate the application of the results obtained.
Topics & Concepts
Korteweg–de Vries equationMathematicsInverse scattering transformPartial differential equationInverse scattering problemOrdinary differential equationClass (philosophy)Operator (biology)Mathematical analysisInverse problemScatteringInverseMathematical physicsApplied mathematicsDifferential equationPhysicsNonlinear systemGeometryQuantum mechanicsChemistryGeneRepressorBiochemistryComputer scienceArtificial intelligenceTranscription factorNonlinear Waves and SolitonsAdvanced Mathematical Physics ProblemsNonlinear Photonic Systems