[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[ 10 ]
[ 11 ]
[ 12 ]
[ 13 ]
[ 14 ]
Candy T. and Lindblad H., Long range scattering for the cubic Dirac equation on R1+1 . Differential Integral Equations 31 (2018), 507–518.
Delort J.-M., Existence globale et comportement asymptotique pour
l’equation de Klein-Gordon quasi lin´eaire `
a donn´ees petites en dimension
1. (French). Ann. Sci. l’Ecole Norm. Sup. (4) 34 (2001), 1–61.
Delort J.-M., Fang D. and Xue R., Global existence of small solutions for
quadratic quasilinear Klein-Gordon systems in two space dimensions. J.
Funct. Anal. 211 (2004), 288–323.
Finkelstein R., Lelevier R. and Ruderman M., Nonlinear spinor fields. Phys.
Rev. 83 (1951), 326–332.
Georgiev V. and Yardanov B., Asymptotic behavior of the one dimensional
Klein-Gordon equation with a cubic nonlinearity, preprint (1996).
Glassey R. T., On the asymptotic behavior of nonlinear wave equations.
Trans. Amer. Math. Soc. 182 (1973), 187–200.
Hayashi N. and Naumkin P. I., The initial value problem for the cubic
nonlinear Klein-Gordon equation. Z. Angew. Math. Phys. 59 (2008), 1002–
1028.
H¨
ormander L., Lectures on nonlinear hyperbolic differential equations.
Math´ematiques & Applications (Berlin), 26. Springer-Verlag, Berlin,
(1997).
Lindblad H. and Soffer A., A remark on asymptotic completeness for the
critical nonlinear Klein-Gordon equation. Lett. Math. Phys. 73 (2005), 249–
258.
Masaki S., Segata J. and Uriya K., Long range scattering for the complexvalued Klein-Gordon equation with quadratic nonlinearity in two dimensions. J. Math. Pures Appl. (9) 139 (2020), 177–203.
Matsumura A., On the asymptotic behavior of solutions of semi-linear wave
equations. Publ. Res. Inst. Math. Sci. 12 (1976/77), 169–189.
Sunagawa H., Remarks on the asymptotic behavior of the cubic nonlinear
Klein-Gordon equations in one space dimension. Differential Integral Equations 18 (2005), 481–494.
Stingo A., Global existence and asymptotics for quasi-linear onedimensional Klein-Gordon equations with mildly decaying Cauchy data.
Bull. Soc. Math. France, 146 (2018), 155–213.
Thirring W. E., A soluble relativistic field theory. Annals of Physics 3
(1958), 91–112.
On the complex valued NLKG in 1D
205
Mathematical Institute
Tohoku University
6-3, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan
E-mail: segata@m.tohoku.ac.jp
Current address:
Faculty of Mathematics
Kyushu University
Fukuoka, 819-0395, Japan
E-mail: segata@math.kyushu-u.ac.jp
...