Scattering operator for the fourth order nonlinear Schrodinger equation

被引：1
|
作者：
Hayashi, Nakao [1 ]
Kawahara, Yuichiro [2 ]
Naumkin, Pavel, I [3 ]
机构：
[1] Tohoku Univ, Res Alliance Ctr Math Sci, Sendai, Miyagi 9808578, Japan
[2] Doshisha Jr & Senior High Sch, Sakyo Ku, Kyoto 6068558, Japan
[3] UNAM, Ctr Ciencias Matemat, Campus Morelia,AP 61-3 Xangari, Morelia 58089, Michoacan, Mexico
来源：
HOKKAIDO MATHEMATICAL JOURNAL | 2021年 / 50卷 / 01期
关键词：
fourth order nonlinear Schrodinger equation; scattering problem; non gauge invariant; WELL-POSEDNESS; ASYMPTOTICS; EXISTENCE;
D O I：
10.14492/hokmj/2018-907
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the fourth order nonlinear Schrodinger equation i partial derivative(t)u - 1/4 partial derivative(4)(omega)u = f(u), (t, x) is an element of R x R) where f(u) is the power nonlinearity of order p > 5. The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.
引用
收藏
页码：91 / 109
页数：19
相关论文
共 50 条
  • [1] Scattering of solutions to the fourth-order nonlinear Schrodinger equation
    Hayashi, Nakao
    Mendez-Navarro, Jesus A.
    Naumkin, Pavel I.
    [J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2016, 18 (03)
  • [2] A fourth-order difference scheme for the fractional nonlinear Schrodinger equation with wave operator
    Pan, Kejia
    Zeng, Jiali
    He, Dongdong
    Zhang, Saiyan
    [J]. APPLICABLE ANALYSIS, 2022, 101 (08) : 2886 - 2902
  • [3] On the inhomogeneous fourth-order nonlinear Schrodinger equation
    Hayashi, Nakao
    Naumkin, Pavel I.
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2015, 56 (09)
  • [4] A NOTE ON FOURTH-ORDER NONLINEAR SCHRODINGER EQUATION
    Saanouni, Tarek
    [J]. ANNALS OF FUNCTIONAL ANALYSIS, 2015, 6 (01) : 249 - 266
  • [5] MODIFIED SCATTERING OPERATOR FOR THE DERIVATIVE NONLINEAR SCHRODINGER EQUATION
    Guo, Zihua
    Hayashi, Nakao
    Lin, Yiquan
    Naumkin, Pavel I.
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (06) : 3854 - 3871
  • [6] Scattering theory for the defocusing fourth-order Schrodinger equation
    Miao, Changxing
    Zheng, Jiqiang
    [J]. NONLINEARITY, 2016, 29 (02) : 692 - 736
  • [7] A new conservative fourth-order accurate difference scheme for the nonlinear Schrodinger equation with wave operator
    Labidi, Samira
    Omrani, Khaled
    [J]. APPLIED NUMERICAL MATHEMATICS, 2022, 173 : 1 - 12
  • [8] Factorization technique for the fourth-order nonlinear Schrodinger equation
    Hayashi, Nakao
    Naumkin, Pavel I.
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (05): : 2343 - 2377
  • [9] Global existence and scattering for a class of nonlinear fourth-order Schrodinger equation below the energy space
    Van Duong Dinh
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 172 : 115 - 140
  • [10] Scattering theory for the fourth-order Schrodinger equation in low dimensions
    Pausader, Benoit
    Xia, Suxia
    [J]. NONLINEARITY, 2013, 26 (08) : 2175 - 2191
12345