Remarks on nonlinear Schrödinger equations in one space dimension

Nakao Hayashi, Tohru Ozawa, J. L. Bona

Research output: Contribution to journalArticlepeer-review

89 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)453-461
Number of pages9
JournalDifferential and Integral Equations
Issue number2
Publication statusPublished - 1994 Mar


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