×

zbMATH — the first resource for mathematics

Stability and instability of traveling solitonic bubbles. (English) Zbl 1033.35117
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.

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
PDF BibTeX XML Cite