Quadratic forms for the 1-D semilinear Schrödinger equation
Open Access
- 1 August 1996
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 348 (8) , 3323-3353
- https://doi.org/10.1090/s0002-9947-96-01645-5
Abstract
This paper is concerned with 1-D quadratic semilinear Schrödinger equations. We study local well posedness in classical Sobolev space H s H^s of the associated initial value problem and periodic boundary value problem. Our main interest is to obtain the lowest value of s s which guarantees the desired local well posedness result. We prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered.Keywords
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