Solutions of the KPI equation with smooth initial data
نویسندگان
چکیده
منابع مشابه
The KP equation with quasiperiodic initial data
The Kadomtsev-Petviashvili (KP) equation is known to admit exact, quasiperiodic solutions that can be written in terms of Riemann theta functions, with a nite number of phases in each solution. In this paper, we propose a method to solve the initial-value problem for the KP equation, for initial data taken from this class of quasiperiodic functions.
متن کاملAsymptotic Solutions of the Two-dimensional Model Wave Equation with Degenerating Velocity and Localized Initial Data
The Cauchy problem is considered for the two-dimensional wave equation with velocity c = √ x1 on the half-plane {x1 ≥ 0, x2}, with initial data localized in a neighborhood of the point (1, 0). This problem serves as a model problem in the theory of beach run-up of long small-amplitude surface waves excited by a spatially localized instantaneous source. The asymptotic expansion of the solution i...
متن کاملRegularity of Solutions to the Free Schrödinger Equation with Radial Initial Data
We derive weighted smoothing inequalities for solutions of the free Schrödinger equation. As an application, we give a new proof of the endpoint Strichartz estimates in the radial case. We also consider general dispersive equations and obtain similar estimates in this case. 0. Introduction Consider the homogeneous initial value problem for the free Schrödinger equation (1) { i∂tu−∆xu = 0, (x, t...
متن کاملTrace identities for solutions of the wave equation with initial data supported in a ball
Suppose u is the solution of the initial value problem utt −∆xu = 0, (x, t) ∈ R × [0,∞); u(x, t=0) = f(x), ut(x, t=0) = g(x), x ∈ R. Suppose n ≥ 1 is odd, f and g are supported in a ball B with boundary S, and one of f or g is zero. We derive identities relating the norm of f or g to the norm of the trace of u on S× [0,∞). These identities are derived using integral geometric and multiplier met...
متن کاملExistence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition
In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Inverse Problems
سال: 1994
ISSN: 0266-5611,1361-6420
DOI: 10.1088/0266-5611/10/3/001