Stuart, David M. A. Modulational approach to stability of non-topological solitons in semilinear wave equations. (English) Zbl 1158.35389 J. Math. Pures Appl. (9) 80, No. 1, 51-83 (2001). The stability properties of a class of solitary wave solutions of the equation \(\square \phi+m^2\phi=\beta(|\phi|)\phi\), where \(\phi:\mathbb{R}^{1+n}\to\mathbb{C}\), are considered in this paper, where solitary waves of the form \(e^{i\omega t}f(x)\) are called non-topological solitons. A modulational approach is developed similar to that used with the nonlinear Schrödinger equation, and novel features are displayed in connection with the \(\omega\)-dependence of the stability condition. It is shown that a stability condition can be derived precisely from the Gagliardo-Nirenberg inequality, while the main result of the paper is a strengthening, for this equation, of existing very general stability results for waves in Hamiltonian systems. Reviewer: Alan Jeffrey (Newcastle upon Tyne) (MR1810509) Cited in 12 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 35B35 Stability in context of PDEs 35Q51 Soliton equations PDF BibTeX XML Cite \textit{D. M. A. Stuart}, J. Math. Pures Appl. (9) 80, No. 1, 51--83 (2001; Zbl 1158.35389) Full Text: DOI OpenURL