Standing waves for a generalized Davey–Stewartson system: Revisited

Standing waves for a generalized Davey-Stewartson system: Revisited

The existence of standing waves for a generalized Davey–Stewartson (GDS) system was shown in Eden and Erbay [8] using an unconstrainted minimization problem. Here, we consider the same problem but relax the condition on the parameters to χ+b < 0 or χ + b m1 < 0. Our approach, in the spirit of Berestycki, Gallouët and Kavian [3] and Cipolatti [6], is to use a constrained minimization problem and...

Standing waves for a two-way model system for water waves

In this paper, we prove the existence of a large family of non-trivial bifurcating standing waves for a model system which describes two-way propagation of water waves in a channel of finite depth or in the near shore zone. In particular, it is shown that, contrary to the classical standing gravity wave problem on a fluid layer of finite depth, the Lyapunov-Schmidt method applies to find the bi...

The Human Heart as a System of Standing Waves

The human heart is considered to be a system of standing waves. Acoustic properties of the human heart are modeled by applying the concepts of wave theory. The nature and the origin of various frequencies are considered. Some experimental suggestions are given.

Standing and travelling waves in a spherical brain model: The Nunez model revisited

The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or an integro-differential equation, have typically been studied in idealised one dimensional or planar settings. Here we revisit the original Nunez m...

Nash-Moser Theory for Standing Water Waves