Modified Scattering Operator for the Derivative Nonlinear Schrödinger Equation

DOI Web Site 被引用文献3件 参考文献16件

書誌事項

公開日
2013-01
資源種別
journal article
DOI
  • 10.1137/12089956x
公開者
Society for Industrial & Applied Mathematics (SIAM)

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説明

We consider the derivative nonlinear Schrodinger equation $i\partial_{t}u+\frac{1}{2}\partial_{x}^{2}u=i\partial_{x}(|u|^{2}u)$, $t\in \mathbf{R}$, $x\in \mathbf{R}$. Our purpose is to prove that the modified scattering operator is defined as a map from the neighborhood of the origin in $\mathbf{H}^{1,\alpha+\gamma}$ to the neighborhood of the origin in $\mathbf{H}^{1,\alpha},$ where $\alpha >\frac{1}{2}$ and $\gamma>0$ is small. The weighted Sobolev space is defined by $\mathbf{H}^{m,s}=\{\phi\in \mathbf{L}^{2};\|(1+x^{2})^{\frac{s}{2}}(1-\partial_{x}^{2})^{\frac{m}{2}}\phi \|_{\mathbf{L}^{2}}<\infty\}.$

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