Exponential Energy Decay for the Kadomtsev-Petviashvili (KP-II) equation
نویسندگان
چکیده
منابع مشابه
Unique Continuation Property for the Kadomtsev-petviashvili (kp-ii) Equation
We generalize a method introduced by Bourgain in [2] based on complex analysis to address two spatial dimensional models and prove that if a sufficiently smooth solution to the initial value problem associated with the Kadomtsev-Petviashvili (KP-II) equation (ut + uxxx + uux)x + uyy = 0, (x, y) ∈ R, t ∈ R, is supported compactly in a nontrivial time interval then it vanishes identically.
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Here u = u(x, y, t) is a scalar function, x and y are respectively the longitudinal and transverse spatial coordinates, subscripts x, y, t denote partial derivatives, and σ2 = ±1. The case σ = 1 is known as the KPII equation, and models, for instance, water waves with small surface tension. The case σ = i is known as the KPI equation, and may be used to model waves in thin films with high surfa...
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A quantisation of the KP equation on a cylinder is proposed that is equivalent to an infinite system of non-relativistic one-dimensional bosons carrying masses m = 1, 2, . . . The Hamiltonian is Galilei-invariant and includes the split Ψ m1 Ψ m2 Ψm1+m2 and merge Ψ m1+m2 Ψm1Ψm2 terms for all combinations of particles with masses m1, m2 and m1 + m2, with a special choice of coupling constants. Th...
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We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form of its tau-function. We show that, in addition to previously known line-soliton solutions, this class also contains a large variety of new multi-soliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general, suc...
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ژورنال
عنوان ژورنال: The São Paulo Journal of Mathematical Sciences
سال: 2011
ISSN: 2316-9028,1982-6907
DOI: 10.11606/issn.2316-9028.v5i2p135-148