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A minimization method and applications to the study of solitons. (English) Zbl 1263.47084

In the paper under review, the authors prove a general abstract theorem that allows to derive existence of a class of solitons related to field equations. Precisely, a solitary wave is a solution of a field equation whose energy travels as a localized packet and which preserves this localization in time. A soliton is a solitary wave which exhibits some strong form of stability so that it has a particle-like behavior. The solitons studied in the paper are suitable minimizers of a constrained functional, and these are called hylomorphic solitons. The abstract theory developed is further applied to problems related to the nonlinear Schrödinger and Klein-Gordon equations.

MSC:

47J30 Variational methods involving nonlinear operators
35J50 Variational methods for elliptic systems
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
47N20 Applications of operator theory to differential and integral equations
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References:

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