TY - JOUR
T1 - On the new critical exponent for the nonlinear Schrödinger equations
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
PY - 2014/1
Y1 - 2014/1
N2 - 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.
AB - 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.
KW - Asymptotics of solutions
KW - New critical exponent
KW - Nonlinear Schrödinger equation
UR - http://www.scopus.com/inward/record.url?scp=84901639293&partnerID=8YFLogxK
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U2 - 10.1007/s00030-013-0252-z
DO - 10.1007/s00030-013-0252-z
M3 - Article
AN - SCOPUS:84901639293
SN - 1021-9722
VL - 21
SP - 415
EP - 440
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
IS - 3
ER -