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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Hydrodynamic reductions: N = 2For N = 2 the system of hydrodynamic laws assumes the <strong>for</strong>m∂ t u 1 = ∂ x (u 1 v 1 ), ∂ t u 2 = ∂ x (u 2 v 2 )u 1 = 1ǫ 12v 2 − ξ 2v 1 − v 2 , u2 = 1ǫ 12v 1 − ξ 1v 2 − v 1 .Passing to the Riemann invariants we obtainv 1 t = v 2 v 1 x , v 2 t = v 1 v 2 x . (1)The system (1) is linearly degenerate, i.e. its characteristic velocities donot depend on the corresponding Riemann invariants.What about N > 2?Gennady El<strong>Kinetic</strong> <strong>equation</strong> <strong>for</strong> a <strong>soliton</strong> <strong>gas</strong>
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