TY - JOUR

T1 - Remarks on nonlinear Schrödinger equations in one space dimension

AU - Hayashi, Nakao

AU - Ozawa, Tohru

AU - Bona, J. L.

PY - 1994/3

Y1 - 1994/3

N2 - We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂x = ∂/∂x and F: C4 → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u0, it is shown that (+) has a unique local solution in time if u0 is in H3, 0 ∩ H2, 1, where Hm, s = {f ∈ S’ ∥f∥m, s = ∥(1 + x2)s/2 (1-Δ)f∥<∞}, m, s ∈ ℝ.

AB - We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂x = ∂/∂x and F: C4 → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u0, it is shown that (+) has a unique local solution in time if u0 is in H3, 0 ∩ H2, 1, where Hm, s = {f ∈ S’ ∥f∥m, s = ∥(1 + x2)s/2 (1-Δ)f∥<∞}, m, s ∈ ℝ.

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M3 - Article

AN - SCOPUS:84972525950

SN - 0893-4983

VL - 7

SP - 453

EP - 461

JO - Differential and Integral Equations

JF - Differential and Integral Equations

IS - 2

ER -