TY - JOUR
T1 - A quadratic nonlinear Schrödinger equation in one space dimension
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
N1 - Funding Information:
We thank a referee for useful comments and suggestions. The work of P.I.N. is partially supported by CONACYT.
PY - 2002/11/20
Y1 - 2002/11/20
N2 - In this paper, we study the Cauchy problem for the quadratic derivative nonlinear Schrödinger equation {iut + UXX = (Ũx)2, (t, x) ε R2, {u(0, x) = u0, x ε R. We suppose that the initial data are small in the weighted Sobolev space H3,1(R) then we prove that there exist global in time small solutions to the Cauchy problem (*). We study the large time behavior of solutions and construct the modified asymptotics for large time values.
AB - In this paper, we study the Cauchy problem for the quadratic derivative nonlinear Schrödinger equation {iut + UXX = (Ũx)2, (t, x) ε R2, {u(0, x) = u0, x ε R. We suppose that the initial data are small in the weighted Sobolev space H3,1(R) then we prove that there exist global in time small solutions to the Cauchy problem (*). We study the large time behavior of solutions and construct the modified asymptotics for large time values.
KW - Large time asymptotics
KW - Nonlinear schrödinger equation
UR - http://www.scopus.com/inward/record.url?scp=0037146377&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037146377&partnerID=8YFLogxK
U2 - 10.1016/S0022-0396(02)00010-4
DO - 10.1016/S0022-0396(02)00010-4
M3 - Article
AN - SCOPUS:0037146377
SN - 0022-0396
VL - 186
SP - 165
EP - 185
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -