Breathers from infinity in the anti-continuum limit - Dmitry Pelinovsky
Breathers from infinity in the anti-continuum limit - Dmitry Pelinovsky
Breathers from infinity in the anti-continuum limit - Dmitry Pelinovsky
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Small-amplitude and large-amplitude brea<strong>the</strong>rsE < 1: There exist two T -periodic even solutions x(t) ∈ Hper 2 (0, T) for T > 2π.The period T = T(E) is at least C 1 .What if E > 1?First answer: No T -periodic solutions exist at all.Second answer:ẍ 0 + V ′ (x 0 ) = 2γ(x 1 − x 0 ) ⇒ ẍ 0 + V γ(x ′ 0 ) = 2γx 1 ,where V γ (x) = V(x) + γx 2 , γ > 0.D.Pel<strong>in</strong>ovsky (McMaster University) <strong>Brea<strong>the</strong>rs</strong> <strong>from</strong> <strong><strong>in</strong>f<strong>in</strong>ity</strong> 8 / 26
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