Inelastic Character of Solitons of Slowly Varying gKdV Equations
نویسندگان
چکیده
منابع مشابه
Refined asymptotics around solitons for gKdV equations
with general C nonlinearity f . Under an explicit condition on f and c > 0, there exists a solution in the energy space H of (0.1) of the type u(t, x) = Qc(x − x0 − ct), called soliton. Stability theory for Qc is well-known. In [11], [14], we have proved that for f(u) = u, p = 2, 3, 4, the family of solitons is asymptotically stable in some local sense in H, i.e. if u(t) is close to Qc (for all...
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with general C nonlinearity f . Under an explicit condition on f and c > 0, there exists a solution in the energy space H of (0.1) of the type u(t, x) = Qc(x − x0 − ct), called soliton. In this paper, under general assumptions on f and Qc, we prove that the family of soliton solutions around Qc is asymptotically stable in some local sense in H , i.e. if u(t) is close to Qc (for all t ≥ 0), then...
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We consider the generalized Korteweg-de Vries equation ∂tu + ∂ 3 xu + ∂x(u ) = 0, (t, x) ∈ R2, in the supercritical case p > 5, and we are interested in solutions which converge to a soliton in large time in H. In the subcritical case (p < 5), such solutions are forced to be exactly solitons by variational characterization [1, 19], but no such result exists in the supercritical case. In this pa...
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We study the problem of 2-soliton collision for the generalized Korteweg-de Vries equations, completing some recent works of Y. Martel and F. Merle [22, 23]. We classify the nonlinearities for which collisions are elastic or inelastic. Our main result states that in the case of small solitons, with one soliton smaller than the other one, the unique nonlinearities allowing a perfectly elastic co...
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We study the dynamics of solitons as solutions to the perturbed KdV (pKdV) equation ∂tu = −∂x(∂ xu + 3u − bu), where b(x, t) = b0(hx, ht), h 1 is a slowly varying, but not small, potential. We obtain an explicit description of the trajectory of the soliton parameters of scale and position on the dynamically relevant time scale δh−1 log h−1, together with an estimate on the error of size h. In a...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2012
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-012-1463-6