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The spectral index is studied at the point where scalar fields deviate from slow-roll during inflation. Considering the deviation that may cause a significant difference to the time derivative of the Hubble parameter and also to the terms…
We examine the regime of validity of $N$-point spectra predictions of single field inflation models that invoke transient periods of non-adiabatic evolution. Such models generate oscillatory features in these spectra spanning frequencies up…
The present work shows that essentially all small-amplitude periodic traveling waves of the electronic Euler-Poisson system are spectrally unstable. This instability is neither modulational nor co-periodic, and thus requires an unusual…
We show that curvature perturbations acquire a scale invariant spectrum for any constant equation of state, provided the fluid has a suitably time-dependent sound speed. In order for modes to exit the physical horizon, and in order to solve…
The Schr\"odinger equation is thoroughly analysed for the isotropic oscillator in the three-dimensional space of constant positive curvature in the spherical and cylindrical systems of coordinates. The expansion coefficients between the…
Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator $H_\epsilon = -\partial_x^2 + x^2 + i\epsilon^{-1}f(x)$ on $L^2(R)$, where $f$ is a real-valued…
We study $I=3/2$ elastic $K\pi $ scattering to Born order using nonrelativistic quark wavefunctions in a constituent-exchange model. This channel is ideal for the study of nonresonant meson-meson scattering amplitudes since s-channel…
This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower order coefficients. The new ingredients of our approach…
In this article we are interested for the numerical computation of spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the location of the…
This paper deals with quantitative spectral stability for compact operators acting on $L^2(X,m)$, where $(X,m)$ is a measure space. Under fairly general assumptions, we provide a characterization of the dominant term of the asymptotic…
The quadratic pion scalar radius, \la r^2\ra^\pi_s, plays an important role for present precise determinations of \pi\pi scattering. Recently, Yndur\'ain, using an Omn\`es representation of the null isospin(I) non-strange pion scalar form…
We consider the following triple power nonlinear Schr{\"o}dinger equation: iut + $\Delta$u + a 1 |u|u + a 2 |u| 2 u + a 3 |u| 3 u = 0. We are interested in algebraic standing waves i.e standing waves with algebraic decay above equation in…
We analytically and numerically investigate the evolutions of the scalar perturbations through the cycles with nonsingular bounce. It is found that the amplitude of the curvature perturbation on large scale will be amplified cycle by cycle,…
The pion scalar radius is given by $<r^2_S>=(6/\pi)\int_{4M^2_\pi}^\infty{\rm d}s \delta_S(s)/s^2$, with $\delta_S$ the phase of the scalar form factor. Below $\bar{K}K$ threshold, $\delta_S=\delta_\pi$, $\delta_\pi$ being the isoscalar,…
We investigate the spectral properties of the Dirichlet Laplacian on large finite metric balls within irregular infinite graphs of quadratic volume growth. We consider an exhaustion $G_n = B_{R_n}(x_0)$ and the spectral zeta value $Z_n(1) =…
The Novikov equation is a peakon equation with cubic nonlinearity which, like the Camassa-Holm and the Degasperis-Procesi, is completely integrable. In this article, we study the spectral and linear stability of peakon solutions of the…
We investigate the spectral instability of a $2\pi/\kappa$ periodic Stokes wave of sufficiently small amplitude, traveling in water of unit depth, under gravity. Numerical evidence suggests instability whenever the unperturbed wave is…
We introduce the notion of spectral points of type $\pi_+$ and type $\pi_-$ of closed operators $A$ in a Hilbert space which is equipped with an indefinite inner product. It is shown that these points are stable under compact perturbations.…
Nonlinear radio waves modulate the plasma, scatter on the modulations, and develop an intermittent power spectrum -- perhaps. Rudiments of theory, numerical simulations, and qualitative modeling of nonlinear scattering are presented.…
The condition of linear instability for a converging cylindrical strong shock wave (SW) in an arbitrary viscous medium is obtained in the limit of a large stationary SW radius, when it is possible to consider the same Rankine-Hugoniot jump…