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Exactly Solvable Models in Mathematical Physics
August 3-8, 1998
South Ural State University
Chelyabinsk, Russia |
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Organizers
Anjan Kundu, Alexander B. Borisov, Arlen M. Il'in, Igor G. Korepanov, Vladimir E. Korepin, Yuri G. Stroganov
View Abstracts
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New soliton-like solutions in sine-Gordon model with infinite discrete spectrum
by
Sergei Zykov
Institute of Metal Physics, S.Kovalevskaya str. 18, 620079, Ekaterinburg, Russia
Coauthors: Alexander B. Borisov
We present a new soliton-like solution of sine-Gordon
equation. For this 'soliton' L-operator of sine-Gordon equation has infinity
discrete spectrum.
The dressing chain of sine-Gordon equation is considered as infinity
dimension system
We use boundary conditions fn+1(x, t)=fn(qx, t/q), \lambdan+1=q\lambdan related
to symmetry of sine-Gordon equation (0 < q < 1). It transform the
dressing chain to system of functional differential equations.
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fx(x, t)+fx(qx, t/q)=q\lambdasinf(qx, t/q)-\lambdasinf(x, t) |
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f(x, t)+f(qx, t/q)=arcsin(q\lambdaft(qx, t/q))-arcsin(\lambdaft(x, t)) |
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Potential u=arcsin(\lambda0 f0, t)-f0 is kink-like
solution of sine-Gordon equation.
L-operator for this potential has self similar spectrum in form
{qn\lambda0|n=1, 2, ..}.
Dynamic of potential, which was studied by numerical calculation, is discussed.
The work was partially supported by RFBR Grant N 97-01-00431.
Date received: July 8, 1998
Copyright © 1998 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caaw-33.