Integrals of motion of the Korteweg–de Vries equation in a class of steplike solutions

1Andreiev, KM
1B.I. Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine, Kharkiv
Dopov. Nac. akad. nauk Ukr. 2016, 9:7-13
https://doi.org/10.15407/dopovidi2016.09.007
Section: Mathematics
Language: Russian
Abstract: 

We study the Cauchy problem for the Korteweg–de Vries with steplike initial data. The regilarized integrals of motion are constructed and expressed via associated scattering data of the Schrödinger equation.

Keywords: integrals of motion, Korteweg–de Vries equation, scattering data
References: 
  1. Egorova I., Teshl G. J. Anal. Math., 2011, 115: No 1: 71–101. https://doi.org/10.1007/s11854-011-0024-9
  2. Andreev K. N., Khruslov E. Ya. Ukr. Mat. Zh., 2015, 67: No 12: 1587–1601 (in Russian).
  3. Lax P. D. Comm. Pure Appl. Math., 1968, 21: No 2: 467–490. https://doi.org/10.1002/cpa.3160210503
  4. Buslaev V. S., Fomin V. N. Vestn. Leningr. Univ., 1962, 17: No 1: 56–64 (in Russian).
  5. Cohen A., Kappeler T. Indiana Univ. Math. J., 1985, 34: 127–180. https://doi.org/10.1512/iumj.1985.34.34008
  6. Egorova I., Gladka Z., Lange T.-L., Teshl G. J. Math. Phys., Anal., Geom., 2015, 11: 123–158.
  7. Hruslov E.J. Math. USSR Sb., 1976, 28: No 2: 229–248. https://doi.org/10.1070/SM1976v028n02ABEH001649
  8. Zakharov V.E., Faddeev L.D. Funct. Anal. Appl., 1971, 5: No 4: 280–287. https://doi.org/10.1007/BF01086739