TY - JOUR
T1 - The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence
AU - Schochet, Steven H.
AU - Weinstein, Michael I.
PY - 1986/12
Y1 - 1986/12
N2 - We consider the initial value problem for the Zakharov equations {Mathematical expression} (x∈ℝk, k=2, 3, t ≧0) which model the propagation of Langmuir waves in plasmas. For suitable initial data solutions are shown to exist for a time interval independent of λ, a parameter proportional to the ion acoustic speed. For such data, solutions of (Z) converge as λ → ∞ to a solution of the cubic nonlinear Schrödinger equation (CSE)iEt+ΔE+|E|2E=0. We consider both weak and strong solutions. For the case of strong solutions the results are analogous to previous results on the incompressible limit of compressible fluids.
AB - We consider the initial value problem for the Zakharov equations {Mathematical expression} (x∈ℝk, k=2, 3, t ≧0) which model the propagation of Langmuir waves in plasmas. For suitable initial data solutions are shown to exist for a time interval independent of λ, a parameter proportional to the ion acoustic speed. For such data, solutions of (Z) converge as λ → ∞ to a solution of the cubic nonlinear Schrödinger equation (CSE)iEt+ΔE+|E|2E=0. We consider both weak and strong solutions. For the case of strong solutions the results are analogous to previous results on the incompressible limit of compressible fluids.
UR - http://www.scopus.com/inward/record.url?scp=0000014949&partnerID=8YFLogxK
U2 - 10.1007/BF01463396
DO - 10.1007/BF01463396
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AN - SCOPUS:0000014949
SN - 0010-3616
VL - 106
SP - 569
EP - 580
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 4
ER -