Search results for "RIEMANN"

Quasi-rational solutions of the NLS equation and rogue waves

2010

We degenerate solutions of the NLS equation from the general formulation in terms of theta functions to get quasi-rational solutions of NLS equations. For this we establish a link between Fredholm determinants and Wronskians. We give solutions of the NLS equation as a quotient of two wronskian determinants. In the limit when some parameter goes to $0$, we recover Akhmediev's solutions given recently It gives a new approach to get the well known rogue waves.

Eighth Peregrine breather solution of the NLS equation and multi-rogue waves

2012

This is a continuation of a paper in which we present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work was based on a recent paper in which we had constructed a multi-parametric family of this equation in terms of wronskians. \\ Here we give a more compact formulation without limit. With this method, we construct Peregrine breather of order N=8 and multi-rogue waves associated by deformation of parameters.

Determinant representation of NLS equation, Ninth Peregrine breather and multi-rogue waves

2012

This article is a continuation of a recent paper on the solutions of the focusing NLS equation. The representation in terms of a quotient of two determinants gives a very efficient method of determination of famous Peregrine breathers and its deformations. Here we construct Peregrine breathers of order $N=9$ and multi-rogue waves associated by deformation of parameters. The analytical expression corresponding to Peregrine breather is completely given.

The design of sum-of-cisoids channel simulators using the iterative nonlinear least square approximation method

2013

In this paper, we propose the iterative nonlinear least square approximation (INLSA) algorithm as an effective method for the design of sum-of-cisoids (SOC) channel simulators assuming non-isotropic scattering conditions. For the characterization of non-isotropic scattering scenarios, we use the von Mises distribution for describing the distribution of the angles-of-arrival (AOAs). The INLSA method relies partially on numerical optimization techniques. This method determines the SOC model parameters iteratively by minimizing the Frobenius error norm. We evaluate the performance of the INLSA method and compare the results with those obtained for the Riemann sum method (RSM) and the Lp-norm m…

Critical point Higgs inflation in the Palatini formulation

2021

We study Higgs inflation in the Palatini formulation with the renormalisation group improved potential in the case when loop corrections generate a feature similar to an inflection point. Assuming that there is a threshold correction for the Higgs quartic coupling $\lambda$ and the top Yukawa coupling $y_t$, we scan the three-dimensional parameter space formed by the two jumps and the non-minimal coupling $\xi$. The spectral index $n_s$ can take any value in the observationally allowed range. The lower limit for the running is $\alpha_s>-3.5\times10^{-3}$, and $\alpha_s$ can be as large as the observational upper limit. Running of the running is small. The tensor-to-scalar ratio is $2.2\tim…

Capturing Shock Reflections: An Improved Flux Formula

1996

Godunov type schemes, based on exact or approximate solutions to the Riemann problem, have proven to be an excellent tool to compute approximate solutions to hyperbolic systems of conservation laws. However, there are many instances in which a particular scheme produces inappropriate results. In this paper we consider several situations in which Roe's scheme gives incorrect results (or blows up all together) and we propose an alternative flux formula that produces numerical approximations in which the pathological behavior is either eliminated or reduced to computationally acceptable levels.

Power ENO methods: a fifth-order accurate Weighted Power ENO method

2004

In this paper we introduce a new class of ENO reconstruction procedures, the Power ENO methods, to design high-order accurate shock capturing methods for hyperbolic conservation laws, based on an extended class of limiters, improving the behavior near discontinuities with respect to the classical ENO methods. Power ENO methods are defined as a correction of classical ENO methods [J. Comput. Phys. 71 (1987) 231], by applying the new limiters on second-order differences or higher. The new class of limiters includes as a particular case the minmod limiter and the harmonic limiter used for the design of the PHM methods [see SIAM J. Sci. Comput. 15 (1994) 892]. The main features of these new ENO…

An asymptotic holomorphic boundary problem on arbitrary open sets in Riemann surfaces

2020

Abstract We show that if U is an arbitrary open subset of a Riemann surface and φ an arbitrary continuous function on the boundary ∂ U , then there exists a holomorphic function φ ˜ on U such that, for every p ∈ ∂ U , φ ˜ ( x ) → φ ( p ) , as x → p outside a set of density 0 at p relative to U . These “solutions to a boundary problem” are not unique. In fact they can be required to have interpolating properties and also to assume all complex values near every boundary point. Our result is new even for the unit disc.

An elliptic equation on n-dimensional manifolds

2020

We consider an elliptic equation driven by a p-Laplacian-like operator, on an n-dimensional Riemannian manifold. The growth condition on the right-hand side of the equation depends on the geometry of the manifold. We produce a nontrivial solution by using a Palais–Smale compactness condition and a mountain pass geometry.

L’idea di iperspazio e l’evoluzione del pensiero geometrico al quadridimensionale

Attraverso un viaggio storico di quasi due secoli, lo scritto vuole analizzare le situazioni in cui lo studio della geometria iperdimensionale ha avuto la sua genesi e la sua evoluzione. Colui il quale approfondisce in modo analitico la questione è Ludwig Schläfli che con il suo Theorie der vielfachen Kontinuität, a partire dallo studio di un integrale, analizza lo spazio pluridimensionale senza cercare una immagine nel mondo circostante di ciò che descrive in modo molto sistematico attraverso i coefficienti che prendono il suo nome. L’aspetto divulgativo della questione viene affrontata a partire dagli anni ’70 del XIX secolo da Beltrami, Casorati e Stringham, da un punto di vista merament…