Stability of Two Soliton Collision for Nonintegrable gKdV Equations
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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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...
متن کاملar X iv : 0 70 9 . 26 77 v 1 [ m at h . A P ] 1 7 Se p 20 07 Stability of two soliton collision for nonintegrable gKdV equations ∗
We continue our study of the collision of two solitons for the subcritical generalized KdV equations ∂tu+ ∂x(∂ 2 xu+ f(u)) = 0. (0.1) Solitons are solutions o the type u(t, x) = Qc0(x− x0 − c0t) where c0 > 0. In [21], mainly devoted to the case f(u) = u, we have introduced a new framework to understand the collision of two solitons Qc1 , Qc2 for (0.1) in the case c2 ≪ c1 (or equivalently, ‖Qc2‖...
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We study confined solutions of certain evolutionary partial differential equations (PDE) in 1 + 1 space–time. The PDE we study are Lie–Poisson Hamiltonian systems for quadratic Hamiltonians defined on the dual of the Lie algebra of vector fields on the real line. These systems are also Euler–Poincaré equations for geodesic motion on the diffeomorphism group in the sense of the Arnold program fo...
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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. 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: Communications in Mathematical Physics
سال: 2008
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-008-0685-0