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On the Convergence of Fourier's Method for Nonlinear Wave‐Envelope Equations
Author(s) -
Gajewski Herbert,
Zacharias Klaus
Publication year - 1979
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19790590105
Subject(s) - envelope (radar) , nonlinear system , mathematical analysis , convergence (economics) , fourier transform , fourier series , mathematics , boundary value problem , split step method , physics , partial differential equation , computer science , telecommunications , radar , quantum mechanics , economics , economic growth
We consider the initial value problem for a system of nonlinear wave‐envelope equations (Zakharov's system) of one‐dimensional plasma physics in the case of spatially periodic boundary conditions. A regularity property of the solution is shown which allows to prove the convergence of the Fourier approximation method.