论文标题
degasperis-procesi方程的光滑孤立波的轨道稳定性
Orbital Stability of smooth solitary waves for the Degasperis-Procesi Equation
论文作者
论文摘要
Degasperis-Procesi方程是可集成的Camassa-Holm型模型，它是浅水波单向传播的渐近近似。这项工作确立了局部平滑孤立波的轨道稳定性，可在真实线上对desgasperis-procesi（DP）方程。 ％将我们先前的工作扩展到其光谱稳定性\ cite {llw}。主要难度源于以下事实：DP方程的翻译对称性产生了相当于$ l^2 $ norm的保守数量，该数量本身无法绑定Lagrangian中的高阶非线性项。补救措施是要观察到，鉴于满足可测量约束的足够光滑的初始条件，扰动的$ l^\ infty $轨道标准在上面是其$ l^2 $轨道标准的函数，从而在$ l^2 \ 2 \ cap l^\ infty $空间中产生轨道稳定性。
The Degasperis-Procesi equation is the integrable Camassa-Holm-type model which is an asymptotic approximation for the unidirectional propagation of shallow water waves. This work establishes the orbital stability of localized smooth solitary waves to the Desgasperis-Procesi (DP) equation on the real line. %extending our previous work on their spectral stability \cite{LLW}. The main difficulty stems from the fact that the translation symmetry for the DP equation gives rise to a conserved quantity equivalent to the $L^2$-norm, which by itself can not bound the higher-order nonlinear terms in the Lagrangian. The remedy is to observe that, given a sufficiently smooth initial condition satisfying a measurable constraint, the $L^\infty$ orbital norm of the perturbation is bounded above by a function of its $L^2$ orbital norm, yielding the orbital stability in the $L^2\cap L^\infty$ space.
