Waves in strongly nonlinear Gardner-like equations on a lattice

On Nonlinear Water Waves in a Channel

Nonlinear waves in a strongly nonlinear resonant granular chain

We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a) small-amplitude periodic traveling waves and (b) dark-breather solutions, i.e., exponentially localized, time periodic states mounted on top of a non-vanish...

Strongly nonlinear waves in capillary electrophoresis.

In capillary electrophoresis, sample ions migrate along a microcapillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background. Under such conditions, the local migration velocity of sample ions becomes concentration-dep...

Strongly Nonlinear Waves in 3d Phononic Crystals

Three dimensional phononic crystal ("sonic vacuum" without prestress) was assembled from 137 vertical cavities arranged in hexagonal pattern in Silicone matrix filled with stainless steel spheres. This system has unique strongly nonlinear properties with respect to wave propagation inherited from nonlinear Hertz type elastic contact interaction. Trains of strongly nonlinear solitary waves excit...

Strongly nonlinear multivalued elliptic equations on a bounded domain

In this work we study the existence of nontrivial solution for the following class of multivalued quasilinear problems −div(φ(|∇u|)∇u)− b(u)u ∈ λ∂F (x, u) in Ω, u = 0 on ∂Ω where Ω ⊂ R is a bounded domain, N ≥ 2 and ∂F (x, u) is a generalized gradient of F (x, t) with respect to t. The main tools utilized are Variational Methods for Locally Lipschitz Functional and a Concentration Compactness T...