TY - JOUR
T1 - Long range scattering for the nonlinear Schrödinger equation with higher order anisotropic dispersion in two dimensions
AU - Saut, Jean Claude
AU - Segata, Jun ichi
N1 - Funding Information:
We thank the referee for careful reading of the manuscript and for fruitful suggestions. Part of this work was done while J.S. was visiting the Department of Mathematics at Université de Paris-Sud, Orsay whose hospitality he gratefully acknowledges. J.S. is partially supported by JSPS , Grant-in-Aid for Scientific Research (B) 17H02851 . J.-C. S. is partly supported by the ANR project ANuI .
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/3/15
Y1 - 2020/3/15
N2 - This paper is a continuation of our previous study [13] on the long time behavior of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion (4NLS). We prove the long range scattering for (4NLS) with the quadratic nonlinearity in two dimensions. More precisely, for a given asymptotic profile u+, we construct a solution to (4NLS) which converges to u+ as t→∞, where u+ is given by the leading term of the solution to the linearized equation of (4NLS) with a logarithmic phase correction.
AB - This paper is a continuation of our previous study [13] on the long time behavior of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion (4NLS). We prove the long range scattering for (4NLS) with the quadratic nonlinearity in two dimensions. More precisely, for a given asymptotic profile u+, we construct a solution to (4NLS) which converges to u+ as t→∞, where u+ is given by the leading term of the solution to the linearized equation of (4NLS) with a logarithmic phase correction.
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U2 - 10.1016/j.jmaa.2019.123638
DO - 10.1016/j.jmaa.2019.123638
M3 - Article
AN - SCOPUS:85074417688
SN - 0022-247X
VL - 483
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 123638
ER -