Regularized Integrals of Motion for the Korteweg–De-Vries Equation in the Class of Nondecreasing Functions

Regularized Integrals of Motion for the Korteweg–De-Vries Equation in the Class of Nondecreasing Functions

We study the Cauchy problem for the Korteweg–de-Vries equation in the class of functions approaching a finite-zone periodic solution of the Korteweg–de-Vries equation as x → − ∞ and 0 as x → + ∞ . We prove the existence of infinitely many “regularized” integrals of motion for the solutions u ( x, t...

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Veröffentlicht in:Ukrainian mathematical journal 2016-05, Vol.67 (12), p.1793-1809
Hauptverfasser: Andreev, K. N., Khruslov, E. Ya
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Zusammenfassung:We study the Cauchy problem for the Korteweg–de-Vries equation in the class of functions approaching a finite-zone periodic solution of the Korteweg–de-Vries equation as x → − ∞ and 0 as x → + ∞ . We prove the existence of infinitely many “regularized” integrals of motion for the solutions u ( x, t ) of the Cauchy problem with explicit dependence on time.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-016-1191-8