Ozawa, Tohru; Tsutsumi, Yoshio The nonlinear Schrödinger limit and the initial layer of the Zakharov equations. (English) Zbl 0754.35163 Differ. Integral Equ. 5, No. 4, 721-745 (1992). It is considered the formation of the convergence of solutions of the Zakharov equations, \[ (1) \quad i(\partial E/\partial t)+\Delta E=nE, \qquad (2) \quad \lambda^{-2}(\partial^ 2n/\partial^ 2t)-\Delta n=\Delta| E|^ 2, \] where \(E\) and \(n\) are functions on the time- space \(R\times R^ N\) with values in \(C^ N\) and \(R\), respectively, in the case when the ion sound speed \(\lambda\) goes to infinity. Analyzing the precise rate of convergence of the solutions as \(\lambda\to\infty\), the authors describe how the solutions of equations (1), (2) tend to the corresponding solutions for the nonlinear Schrödinger equation, the latter is known to have unique solutions, and it is exactly integrable by the inverse scattering transform. Reviewer: Y.Kivshar (Düsseldorf) Cited in 1 ReviewCited in 42 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 76F99 Turbulence 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems Keywords:uniqueness of solutions; inverse scattering transform × Cite Format Result Cite Review PDF