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math.AP2017★ 12 cited
Invariant Manifolds of traveling waves of the 3D Gross-Pitaevskii equation in the energy space
Jiayin Jin, Zhiwu Lin, Chongchun Zeng
We study the local dynamics near general unstable traveling waves of the 3D Gross-Pitaevskii equation in the energy space by constructing smooth local invariant center-stable, cent…
math.AP2017★ 19 cited
Nonlinear Modulational Instability of Dispersive PDE Models
Jiayin Jin, Shasha Liao, Zhiwu Lin
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations…