Kinetic equation for a soliton gas - SOLITONS, COLLAPSES AND ...
Kinetic equation for a soliton gas - SOLITONS, COLLAPSES AND ...
Kinetic equation for a soliton gas - SOLITONS, COLLAPSES AND ...
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Future researchConnection with hydrodynamic chains and 2+1 dispersionlesssystems.Motivation: The collisionless Boltzmann kinetic <strong>equation</strong> <strong>for</strong> thedistribution function f (p, x, t)∂f∂t + p ∂f (∫ ) ∂f ∂f∂x − ∂x dp ∂p = 0is equivalent to the Benney moment chain (Zakharov 1981, Gibbons1981)∂A n+ ∂A ∫n+1 ∂A 0+ nA n−1∂t ∂x ∂x = 0 , A n = p n fdpand to the dispersionless KP-II <strong>equation</strong> (Kupershmidt & Manin ??,Gibbons 1984, Kodama 1988)(u t + 6uu x ) x + u yy = 0 .Construction of physically relevant exact solutions.PDF, correlation function.Gennady El<strong>Kinetic</strong> <strong>equation</strong> <strong>for</strong> a <strong>soliton</strong> <strong>gas</strong>
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