Abstract
We consider the Cauchy problem for the pth order nonlinear Schrödinger equation in one space dimension (Formula presented.) where (Formula presented.). We reveal that p = 4 is a new critical exponent with respect to the large time asymptotic behavior of solutions. We prove that if ps < p < 4, then the large time asymptotics of solutions essentially differs from that for the linear case, whereas it has a quasilinear character for the case of p > 4.
Original language | English |
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Pages (from-to) | 415-440 |
Number of pages | 26 |
Journal | Nonlinear Differential Equations and Applications |
Volume | 21 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2014 Jan |
Externally published | Yes |
Keywords
- Asymptotics of solutions
- New critical exponent
- Nonlinear Schrödinger equation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics