Related papers: Stationary Bohmian superposition under amplitude a…
The Ermakov Pinney equation and its associated invariant are shown to arise naturally in stationary quantum mechanics when the Schrodinger equation is expressed in Bohm Madelung form and the Hamiltonian is diagonal and separable. Under…
We employ weakly nonlinear theory to derive an amplitude equation for the conserved-Hopf instability, i.e., a generic large-scale oscillatory instability for systems with two conservation laws. The resulting equation represents in the…
This work investigates the dynamics of a charged particle in a uniform magnetic field within the Bohm--Madelung formulation of quantum mechanics. In this representation, the stationary Schrodinger equation separates into coupled amplitude…
We consider a version of the stationary phase method in one dimension of A. Erd\'elyi, allowing the phase to have stationary points of non-integer order and the amplitude to have integrable singularities. We provide a complete proof and we…
Weakly non-linear stability of regimes of free hydromagnetic thermal convection in a rotating horizontal layer with free electrically conducting boundaries is considered in the Boussinesq approximation. Perturbations are supposed to involve…
Boussinesq-type wave equations involve nonlinearities and dispersion. In this paper a Boussinesq-type equation with amplitude-dependent nonlinearities is presented. Such a model was proposed by Heimburg and Jackson (2005) for describing…
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this…
Many field theories of physical interest have configuration spaces consisting of disconnected components. Quantum mechanical amplitudes are then expressed as sums over these components. We use the Faddeev-Popov approach to write the terms…
This technical note is a complement to an earlier paper [Benzoni-Gavage \& Rosini, Comput. Math. Appl. 2009], which aims at a deeper understanding of a basic model for propagating phase boundaries that was proved to admit surface waves…
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' $q$-nonextensive statistics.…
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to…
A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions…
We describe and demonstrate a method to reconstruct an amplitude equation from the nonlinear relaxation dynamics in the succession of the Rosensweig instability. A flat layer of a ferrofluid is cooled such that the liquid has a relatively…
Avoided crossings (A.C.) in open resonators arise from non-Hermitian mode interaction, where leakage produces complex spectra and biorthogonal eigenmodes. Intensity-based entropies are robust markers of mode mixing but discard the phase…
Modular variables serve as a striking example of quantum nonlocality, particularly in superpositions of wave packets that are spatially well separated, where the relative phase between components cannot be accessed through conventional…
The principle of stationary phase (PSP) is re-examined in the context of linear time-frequency (TF) decomposition using Gaussian, gammatone and gammachirp filters at uniform, logarithmic and cochlear spacings in frequency. This necessitates…
We present a new type of phase- and frequency-sensitive amplification and attenuation in a cyclically driven three-level superconducting Josephson system. Different from the previous linear theory of pure phase-sensitive amplification, a…
In the present work, we establish the approximation of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical {\alpha}-stable L\'evy processes via modulation or amplitude equations. We study SPDEs with a cubic…
We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form $\amp{\psi_f}{\psi}$, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$…
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…