Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
- 1 November 1984
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 25 (11) , 3270-3273
- https://doi.org/10.1063/1.526074
Abstract
Let u be a nontrivial, smooth solution to iut=Δu−‖u‖ p−1u. If n=1 and 2<p≤3, then there does not exist any finite energy free solution v such that ∥u(t)−v(t)∥2→0 as t→+∞. This extends a theorem of Strauss in which the same result was proved for 1<p≤2.Keywords
This publication has 1 reference indexed in Scilit:
- On the asymptotic behavior of nonlinear wave equationsTransactions of the American Mathematical Society, 1973