Related papers: Solitary magnetostrophic Rossby waves in spherical…
This paper is devoted to the study of solitary waves and solitons whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the Q-balls, which are spherically symmetric solutions…
The Rossby wave instability in astrophysical disks is as a potentially important mechanism for driving angular momentum transport in disks. We aim to understand this instability in an approximate three-dimensional disk model environment…
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 show existence of small solitary and periodic traveling-wave solutions in Sobolev spaces ${\mathrm{H}^s}$, ${ s > 0 }$, to a class of nonlinear, dispersive evolution equations of the form \begin{equation*} u_t + \left(Lu+ n(u)\right)_x =…
The theory of waves and instabilities in a differentially rotating disc containing a poloidal magnetic field is developed within the framework of ideal magnetohydrodynamics. A continuous spectrum, for which the eigenfunctions are localized…
This work studies the rotation-generalized Benjamin-Ono equation which is derived from the theory of weakly nonlinear long surface and internal waves in deep water under the presence of rotation. It is shown that the solitary-wave solutions…
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, discrete, homogeneous chains with a general power-law contact interaction is studied. For this wave equation,…
The nonlinear excitations underlying the onset of rotation in a dilute Bose-Einstein condensate confined to a thin spherical shell are studied. These excitations correspond to solitary waves rotating about the sphere at constant angular…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
We consider a family of globally stationary (horizonless), asymptotically flat solutions of five-dimensional supergravity. We prove that massless linear scalar waves in such soliton spacetimes cannot have a uniform decay rate faster than…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…
A Rossby-Haurwitz (RH) wave is an excitation mode of a fluid on a rotating spherical surface, which propagates westward in the rotating frame of reference. Motivated by the recent realization of the shell-shaped Bose-Einstein condensate in…
Seismic waves sensitive to the outermost part of the Earth's liquid core seem to be affected by a stably stratified layer at the core-mantle boundary. Such a layer could have an observable signature in both long-term and short-term…
The MHD slow mode wave has application to coronal seismology, MHD turbulence, and the solar wind where it can be produced by parametric instabilities. We consider analytically how a drifting ion species (e.g. He$^{++}$) affects the linear…
The paper deals with the studies of the nonlinear wave solutions supported by the modified FitzHugh-Nagumo (mFHN) system. It was proved in our previous work that the model, under certain conditions, possesses a set of soliton-like traveling…
Periodic waves in the fractional Korteweg-de Vries equation have been previously characterized as constrained minimizers of energy subject to fixed momentum and mass. Here we characterize these periodic waves as constrained minimizers of…
The effect of the modulation instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schr\"odinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed…
Recent observations of Rossby waves and other more exotic forms of inertial oscillations in the Sun's convection zone have kindled the hope that such waves might be used as a seismic probe of the Sun's interior. Here we present a 3D…
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence for water of finite depth has recently…
We prove the existence of a new type of solutions to a nonlinear Schr\"odinger system. These solutions, which we call "multi-speeds solitary waves", are behaving at large time as a couple of scalar solitary waves traveling at different…