Long time behavior of the NLS-Szegő equation
نویسندگان
چکیده
منابع مشابه
Long–time Asymptotics for the Nls Equation via ∂̄ Methods
−∞ log(z− s)d(log(1−|r(s)|2))+ π 4 + argΓ(iν(z))− argr(z). Here z0 = −x/(4t), Γ is the gamma function and the function r is the so-called reflection coefficient associated to the initial data q0, as described later in this section. Estimates on the size of the error term E (x,t) depend on the smoothness assumptions on q0. The above asymptotic form was first obtained in [10]. The nonlinear steep...
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Here Γ is the gamma function and the function r is the so-called reflection coefficient for the potential q0(x) = q(x, t = 0), as described below. The error term O( log t t ) is uniform for all x ∈ R. The above asymptotic form was first obtained in [ZaMa], but without the error estimate. Based on the nonlinear steepest descent method introduced in [DZ1], the error estimate in (1.1) was derived ...
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ژورنال
عنوان ژورنال: Dynamics of Partial Differential Equations
سال: 2019
ISSN: 1548-159X,2163-7873
DOI: 10.4310/dpde.2019.v16.n4.a2