Scattering of solutions with group invariance for the fourth-order nonlinear Schrödinger equation

被引：0

作者：

Komada, Koichi ^{[1
]}

Masaki, Satoshi ^{[2
]}

机构：

[1] Ritsumeikan Univ, Ritsumeikan Global Innovat Res Org, Kusatsu, Shiga 5258577, Japan

[2] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

来源：

NONLINEARITY | 2024年 / 37卷 / 08期

关键词：

fourth-order nonlinear Schr & ouml; dinger equation; scattering theory; group invariance; profile decomposition; GLOBAL WELL-POSEDNESS; SCHRODINGER-EQUATION; BLOW-UP; DYNAMICS;

D O I：

10.1088/1361-6544/ad5639

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the focusing, L 2-supercritical and H (center dot) 2 -subcritical fourth-order nonlinear Schr & ouml;dinger equations. We show the scattering of group-invariant solutions below the ground state threshold, under the hypothesis that the threshold for group-invariant solutions is less than a certain value.

引用

页数：38

共 50 条

[21] Global existence of odd solutions for the cubic fourth-order nonlinear Schrödinger equationsCubic fourth-order Schrödinger equationsN. Hayashi and P. I. Naumkin
Nakao Hayashi
Pavel I. Naumkin
Nonlinear Differential Equations and Applications NoDEA, 2025, 32 (3)
[22] The fourth-order nonlinear Schrödinger limit for quantum Zakharov system
Yung-Fu Fang
Chi-Kun Lin
Jun-Ichi Segata
Zeitschrift für angewandte Mathematik und Physik, 2016, 67
[23] Jacobi elliptic solutions, solitons and other solutions for the nonlinear Schrödinger equation with fourth-order dispersion and cubic-quintic nonlinearity
Elsayed M. E. Zayed
Abdul-Ghani Al-Nowehy
The European Physical Journal Plus, 132
[24] Instability of single- and double-periodic waves in the fourth-order nonlinear Schrödinger equation
N. Sinthuja
S. Rajasekar
M. Senthilvelan
Nonlinear Dynamics, 2023, 111 : 16497 - 16513
[25] Split-step multisymplectic integrator for fourth-order Schrödinger equation with cubic nonlinear term
Kong, Linghua
Cao, Ying
Wang, Lan
Wan, Long
Jisuan Wuli/Chinese Journal of Computational Physics, 2011, 28 (05): : 730 - 736
[26] Jacobian elliptic wave trains in fourth-order dispersive nonlinear Schrödinger equation and the modulational instability
Raju T.S.
Triki H.
Optik, 2024, 302
[27] Numerical investigation of solitary-wave solutions for the nonlinear Schrödinger equation perturbed by third-order and negative fourth-order dispersion
Melchert, Oliver
Demircan, Ayhan
PHYSICAL REVIEW A, 2024, 110 (04)
[28] Localized wave solutions to coupled variable-coefficient fourth-order nonlinear Schrödinger equations
Song, N.
Guo, M. M.
Liu, R.
Ma, W. X.
MODERN PHYSICS LETTERS A, 2024, 39 (09)
[29] Global well-posedness for nonlinear fourth-order Schrödinger equations
Xiuyan Peng
Yi Niu
Jie Liu
Mingyou Zhang
Jihong Shen
Boundary Value Problems, 2016
[30] Bright, dark, and periodic soliton solutions for the (2+1)-dimensional nonlinear Schrödinger equation with fourth-order nonlinearity and dispersion
Ali, Khalid K.
Mohamed, Mohamed S.
Mehanna, M. S.
OPTICAL AND QUANTUM ELECTRONICS, 2024, 56 (06)

← 1 2 3 4 5 →