On the Inelastic Two-Soliton Collision for gKdV Equations with General Nonlinearity
نویسندگان
چکیده
منابع مشابه
On the Inelastic 2-soliton Collision for Gkdv Equations with General Nonlinearity
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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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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For the L subcritical and critical (gKdV) equations, Martel [11] proved the existence and uniqueness of multi-solitons. Recall that for any N given solitons, we call multi-soliton a solution of (gKdV) which behaves as the sum of these N solitons asymptotically as t → +∞. More recently, for the L supercritical case, Côte, Martel and Merle [4] proved the existence of at least one multi-soliton. I...
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متن کاملRefined 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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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2009
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnp204