Segregated solutions for nonlinear Schr\"odinger systems with a large number of components

In this paper we are concerned with the existence of segregated non-radial solutions for nonlinear Schr\"odinger systems with a large number of components in a weak fully attractive or repulsive regime in presence of a suitable external radial potential

Segregated solutions for some non-linear Schr\"odinger systems with critical growth

We find infinitely many positive non-radial solutions for a system of Schr\"odinger equations with critical growth in a fully attractive or repulsive regime in presence of an external radial trapping potential.Comment: 28 page

The Nonlinear Talbot Effect of Rogue Waves

Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schr\"odinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a \pi-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.Comment: 4 pages, 4 figure

Existence and multiplicity of peaked bound states for nonlinear Schr\"odinger equations on metric graphs

We establish existence and multiplicity of one-peaked and multi-peaked positive bound states for nonlinear Schr\"odinger equations on general compact and noncompact metric graphs. Precisely, we construct solutions concentrating at every vertex of odd degree greater than or equal to $3$. We show that these solutions are not minimizers of the associated action and energy functionals. To the best of our knowledge, this is the first work exhibiting solutions concentrating at vertices with degree different than $1$. The proof is based on a suitable Ljapunov-Schmidt reduction.Comment: 25 pages, 2 figure

Could the UK’s monetary policy be improved by targeting nominal GDP? A model of the UK with state-dependent price/wage contracts

There is substantial evidence from both macro and micro data that the durations of price/wage contracts vary with the state of the economy, particularly with inflation. This thesis investigates whether there is macro-level evidence of state-dependent price/wage contracts in the UK and examines the policy implications of a UK macroeconomic model in the presence of state-dependent variation. Two versions of the price/wage-setting framework are considered in this thesis: a fixed price/wage contract duration framework and a state-dependent duration framework. Each framework is incorporated into an open economy Dynamic Stochastic General Equilibrium (DSGE) model. It combines the New Keynesian and New Classical models into a hybrid model, incorporates financial friction, and includes several new developments in the wake of the recent Great Financial Crisis, including allowing for zero lower bound and quantitative easing. The fixed duration and state-dependent models are tested and estimated over the whole sample period 1955-2021 for the UK macroeconomic data using a simulation-based Indirect Inference method. The main findings of this thesis are: 1) the fixed duration model fits the behaviour of the UK data for the inflation targeting era 1992-2021, but not for the whole sample period 1955-2021; 2) The state-dependent model fits the behaviour of the UK historical data well over the whole sample period 1955-2021, implying that the state-dependent price/wage contract framework improves the fit of the DSGE model to the macroeconomic data. Furthermore, the durations of price/wage contracts fluctuate with the state of the economy (especially inflation) throughout the whole sample period; 3) A nominal GDP targeting rule together with a fiscal backstop to prevent zero lower bound can reduce the chances of economic crisis and stabilise the UK macroeconomy. Therefore, it outperforms the Taylor Rule regime