Stability theory for solitary-wave solutions of scalar field equations
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Publication:798532
DOI10.1007/BF01208719zbMath0546.35062OpenAlexW1989700845MaRDI QIDQ798532
J. Fernando Perez, Walter F. Wreszinski, Daniel B. Henry
Publication date: 1982
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01208719
Stability in context of PDEs (35B35) Fixed-point theorems (47H10) Partial differential equations of mathematical physics and other areas of application (35Q99)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stability for the Korteweg-de Vries equation by inverse scattering theory
- Properties of infinite dimensional Hamiltonian systems
- The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
- Hilbert space sectors for solutions of non-linear relativistic equations
- Existence of solitary waves in higher dimensions
- Integrals of nonlinear equations of evolution and solitary waves
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