In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field V on an open subset of C and a discrete set Y âŠ‚ R with n elements, we define aâ€¦ (More)

We study the point limit of the linearized Maxwell{Lorentz equations describing the interaction, in the dipole approximation, of an extended charged particle with the electromagnetic eld. We nd thatâ€¦ (More)

In this paper, an introduction to the new subject of nonlinear dispersive Hamiltonian equations on graphs is given. The focus is on recently established properties of solutions in the case of theâ€¦ (More)

We consider the problem of nding rigorous results for the dynamics of a classical charged point particle interacting with the electromagnetic eld, as described by the standard Maxwell{Lorentzâ€¦ (More)

Physical review. E, Statistical, nonlinear, andâ€¦

2015

In this paper we give the complete classification of solitons for a cubic nonlinear SchrÃ¶dinger equation on the simplest network with a nontrivial topology: the tadpole graph, i.e., a ring with aâ€¦ (More)

We define and study the Cauchy problem for a one-dimensional (1-D) nonlinear Dirac equation with nonlinearities concentrated at one point. Global well-posedness is provided and conservation laws forâ€¦ (More)

We continue in this paper the analysis, begun in NP], of the classical dynamics of the point limit of the Maxwell{Lorentz system in dipole approximation (the Pauli{Fierz model). Here, as a rst stepâ€¦ (More)

We develop a detailed analysis of edge bifurcations of standing waves in the nonlinear SchrÃ¶dinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to the Kirchhoffâ€¦ (More)