The dynamics of interacting solitons for the Korteweg-de Vries equation

• Autorzy: Olejniczak M. , Błaszak M.
• Konferencja: Jubilee Symposium Vibrations In Physical Systems (25 ; 15-19.05.2012 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

The aim of the paper is to give a new insight into the interaction of soliton particles and their dynamics. We introduce the definition of a soliton, soliton particles (interacting solitons) and a theorem about the decomposition of multi-soliton solutions to soliton particles. In the paper we also give a theorem state that the motion of maxima of interacting solitons (in a special case) are roots of fourth order polynomial.

Słowa kluczowe

EN

solitons; interacting solitons; dynamics

PL

solitony; interakcja solitonów; dynamika

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2012
• Tom: Vol. 25
• Strony: 311--316
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Olejniczak M.

• Institute of Applied Mechanics, Poznan University of Technology, ul. Jana Pawła II 24, 60-965 Poznan, Poland

autor

Błaszak M.

• Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznan, Poland

Bibliografia

• 1. Mark J. Ablowitz, Harvey Segur, Solitons and the Inverse Scattering Transform, SIAM Studies in Applied Mathematics, 1981
• 2. Nicholas Benes, Alex Kasman, Kevin Young, On decomposition of the KdV 2-soliton, Journal of Nonlinear Science, 16(2):179-200, April 2006
• 3. Maciej Błaszak, On interacting solitons, Acta Phys. Polon, A74:439, 1988
• 4. Maciej Błaszak, Theory of classical soliton particles, UAM Press, 1989
• 5. Maciej Błaszak, Multi-Hamiltonian Theory of Dynamics Systems, Texts and Monographs in Physics, Springer-Verlag, 1998
• 6. P.G. Drazin, R.S. Johnson, Soliton: an introduction/ P.G. Drazin/R.S. Johnson, Cambridge University Press, Cambridge, New York 1989
• 7. Benno Fuchssteiner, The Lie algebra structure of nonlinear evolution equations admitting infinite dimensional abelian symmetry group, Progress of Theoretical Physics, 65(3), March 1981
• 8. Benno Fuchssteiner, The dynamical behaviour of interacting solitons, In Nonlinear Evolutions, pages 13-32, World Scientific Publishers, 1988
• 9. J. Hietarinta, Introduction to the Hirota bilinear method, August 1997
• 10. Peter J. Olver, Applications of Lie group to differential equations, Springer, 2 editions, 1993
• 11. John Parkers, Fiona Campbell, The internal structure of two-soliton solution to nonlinear evolutions equations of a certain class, SOLPHYS, 1997
• 12. Y. P. Rybakov, B. Saha, Soliton model of atom, Foundation of Physics, 25:1723-1731, December 1995.