There exist dipole solutions to the Klein-Gordon-Zakharov system consisting of two solitary waves whose positions satisfy |z1(t) - z2(t)| ~ 2 log(t) as t → ∞.
Miura, The Korteweg–deVries equation: a survey of results, SIAM Review 18 (1976) 412–459.↑2
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Existence of dipoles of Klein-Gordon-Zakharov system
There exist dipole solutions to the Klein-Gordon-Zakharov system consisting of two solitary waves whose positions satisfy |z1(t) - z2(t)| ~ 2 log(t) as t → ∞.