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Stability of the soliton-like “bubbles”. (English) Zbl 0697.35127
Summary: We show that the recently found bubble-like soliton solutions of D- dimensional nonlinear Schrödinger (NLS) equation are unstable for any D and that this fact does not depend on the choice of nonlinearity. For the particular case of the \(\psi^ 3-\alpha \psi^ 5\) NLS equation which arises in a variety of physical contexts the bubble’s growth rates are numerically calculated.

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35B35 Stability in context of PDEs
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