Lin, Zhiwu Stability and instability of traveling solitonic bubbles. (English) Zbl 1033.35117 Adv. Differ. Equ. 7, No. 8, 897-918 (2002). Summary: We study the nonlinear Schrödinger equation with general nonlinearity of competing type. This equation has traveling waves solution with non-vanishing condition at infinity in one dimension. We give a sharp condition for the stability and instability of these solutions. This justifies previous predictions in physical literature. Cited in 24 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems 35B35 Stability in context of PDEs 35Q51 Soliton equations Keywords:nonlinear Schrödinger equation; traveling waves solution; stability; instability PDFBibTeX XMLCite \textit{Z. Lin}, Adv. Differ. Equ. 7, No. 8, 897--918 (2002; Zbl 1033.35117)