Related papers: On the homotopy multiple-variable method and its a…
Wave kinetic theory for rapidly rotating flows is developed in this paper using a rigorous application of multiple scales perturbation theory. The governing equations are an asymptotically reduced set of equations that are derived from the…
The dispersion relation of surface waves of a magnetic fluid in a magnetic field is studied experimentally. We verify the theoretically predicted existence of a non-monotonic dispersion relation. In particular, we demonstrate the existence…
We comment on some analytical solutions to a class of Boussinesq-like equations derived recently by means of the homotopy perturbation method (HPM). We show that one may obtain exactly the same result by means of the Taylor series in the…
In propagating wave systems, three or four-wave resonant interactions constitute a classical non-linear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface…
Apart from omnidirectional, a solid elastic sphere is a natural multimode and multifrequency device for the detection of Gravitational Waves (GW). Motion sensing in a spherical GW detector thus requires a multiple set of transducers…
We consider a general model of Hamiltonian wave systems with triple resonances, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. In this asymptotic limit we show that the correct…
The purpose of this work is to introduce a concept of traveling waves in the setting of periodic metric graphs. It is known that the nonlinear Schr{\"o}dinger (NLS) equation on periodic metric graphs can be reduced asymptotically on long…
We develop a coordinate invariant formalism which describes the mechanical and electromagnetic interaction of gravitational waves (GWs) with a wide class of resonant detectors. We solve the GW-modified equations of electrodynamics and…
Wilton ripples are a type of periodic traveling wave solution of the full water wave problem incorporating the effects of surface tension. They are characterized by a resonance phenomenon that alters the order at which the resonant harmonic…
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of…
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…
In this paper we address the stability of resonantly forced density waves in dense planetary rings. Already by Goldreich & Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the…
In this paper, we study two-dimensional steady solitary gravity waves propagating along the surface of a fluid of finite depth. In particular, we can deal with general vorticity distributions and overhanging wave profiles. By conformal…
In this study, we present several improvements of the non-relativistic Friedrichs-Lee model with multiple discrete and continuous states and still retain its solvability. Our findings establish a solid theoretical basis for the exploration…
The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the…
Solution of the Dyson equation for the small-gap systems can be plagued by large non-converging iterations. In addition to the convergence issues, due to a high non-linearity, the Dyson equation may have multiple solutions. We apply the…
In this paper, we initiate the study of the global stability of nonlinear wave equations with initial data that are not required to be localized around a single point. More precisely, we allow small initial data localized around any finite…
Nonlinear modal interactions in resonant systems govern a wide range of phenomena, with broad relevance across modern physics and engineering. Yet, experimentally determining the strength of nonlinear coupling in multimode resonators…
We propose an analytical framework to model the effect of single and multiple mechanical surface oscillators on the dynamics of vertically polarized elastic waves propagating in a semi-infinite medium. The formulation extends the canonical…
In this paper, we present a model describing the time evolution of two dimensional surface waves in gravity and infinite depth. The model of six interacting modes derives from the normal form of the system describing the dynamics of surface…