Contents/conteúdo

Lisbon WADE — Webinar in Analysis and Differential Equations   RSS

Rainer Mandel 12/11/2020, 14:30 — 15:30 — Room P1, Mathematics Building Online
, Karlsruhe Institute of Technology

New dual variational methods for Nonlinear Helmholtz Equations and polychromatic solutions of Nonlinear wave equations

In the first part of my talk, I present the classical dual variational method in the context of Nonlinear Helmholtz equations that describe monochromatic waves in nonlinear materials. Afterwards, I discuss two recent generalizations of the method. The first deals with an extension to Nonlinear Helmholtz equations with sign-changing nonlinearities. For these problems we construct solutions that have infinite Morse-Index in the dual variational formulation. The second generalization concerns dual variational methods for the construction of breathers, i.e., polychromatic, spatially localized and time-periodic solutions of nonlinear wave equations.

The results were obtained in collaboration with D. Scheider and T. Yesil.

Projecto FCT UIDB/04459/2020.

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Organizers: Hugo Tavares, James Kennedy and Nicolas Van Goethem

Joint iniciative of the research centers CAMGSD, CMAFcIO and GFM.

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