Null Structure in a System of Quadratic Derivative Nonlinear Schrodinger Equations

Ikeda Masahiro; Katayama Soichiro; Sunagawa Hideaki

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Null Structure in a System of Quadratic Derivative Nonlinear Schrodinger Equations

机译：二次微分非线性薛定inger方程组的零结构

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We consider the initial value problem for a three-component system of quadratic derivative nonlinear Schrodinger equations in two space dimensions with the masses satisfying the resonance relation. We present a structural condition on the nonlinearity under which small data global existence holds. It is also shown that the solution is asymptotically free. Our proof is based on the commuting vector field method combined with smoothing effects.

机译：我们考虑质量满足共振关系的二维空间三阶二次非线性非线性薛定inger方程的三元系统的初值问题。我们提出了一个非线性的结构条件，在该条件下，小数据全局存在。还表明该解决方案是渐近自由的。我们的证明是基于通勤矢量场方法并结合了平滑效果。

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《Annales Henri Poincare》 |2015年第2期|共33页
作者
Ikeda Masahiro; Katayama Soichiro; Sunagawa Hideaki;
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中图分类理论物理学;
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1. Null Structure in a System of Quadratic Derivative Nonlinear Schrodinger Equations [J] . Ikeda Masahiro, Katayama Soichiro, Sunagawa Hideaki Annales Henri Poincare . 2015,第2期

机译：二次微分非线性薛定inger方程组的零结构
2. Well-Posedness for a System of Quadratic Derivative Nonlinear Schrodinger Equations with Radial Initial Data [J] . Hirayama Hiroyuki, Kinoshita Shinya, Okamoto Mamoru Annales Henri Poincare . 2020,第8期

机译：具有径向初始数据的二次衍生非线性Schrodinger方程的良好良好
3. Sharp bilinear estimates and its application to a system of quadratic derivative nonlinear Schrodinger equations [J] . Hirayama Hiroyuki, Kinoshita Shinya Nonlinear Analysis: An International Multidisciplinary Journal . 2019,第期

机译：尖锐的双线性估计及其在二次衍生非线性薛定格格方程系统中的应用
4. Nonlinear Optical Output of Atomic Systems via Numerical Simulation of Time-Dependent Schrodinger Equations, Stimulated by Laser Sources, in and out of Resonance Conditions within the Non-Perturbative Regime [C] . Stephen Karasek, Charles DiMarzio Three-dimensional and multidimensional microscopy: image acquisition and processing XXII . 2015

机译：原子系统的非线性光输出，通过时变薛定Reg方程的数值模拟（由激光源激发）在非扰动范围内进入和离开共振条件进行
5. New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions [D] . Tanguay, Allison J. 2012

机译：用于2 + 1维度的二次衍生非线性波方程的新Bilinear估计
6. On Coupled Rate Equations with Quadratic Nonlinearities [O] . Elliott W. Montroll 1972

机译：具有二次非线性的耦合速率方程
7. Null structure in a system of quadratic derivative nonlinear Schr"odinger equations [O] . Ikeda, Masahiro, Katayama, Soichiro, Sunagawa, Hideaki 2013

机译：二次导数非线性系统的零结构 schr \“odinger方程
8. Quadratic Bundle of General Form and the Nonlinear Evolution Equations. Hierarchies of Hamiltonian Structures [R] . Gerdjikov, V. S., Ivanov, M. I. 1982

机译：一般形式的二次束与非线性发展方程。哈密顿结构的层次结构

Null Structure in a System of Quadratic Derivative Nonlinear Schrodinger Equations

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