We study the existence of liquefaction and evaporation waves by the methods derived from dynamical systems theory. A traveling wave solution is a heteroclinic orbit with the wave speed as a parameter. We give sufficient and necessary conditions for the existence of such heteroclinic orbit. After analyzing the local unstable and stable manifolds of two equilibrium points, we show that there exis...

The stability of the bright solitary wave solution to the perturbed cubicquintic Schrödinger equation is considered. It is shown that in a certain region of parameter space these solutions are unstable, with the instability being manifested as a small positive eigenvalue. Furthermore, it is shown that in the complimentary region of parameter space there are no small unstable eigenvalues. The pr...

In this paper we consider the in mal signal-to-noise ratio (SNR) required for stabilisation of a linear time invariant (LTI) scalar unstable plant over a class of additive colouredGaussian noise channels. We apply recent results in the literature to obtain the feedback capacity of such a class of channels. We prove that the in mal SNR constrained LTI solution, when dealing with a scalar unstabl...

Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of variational sampling (i.e., combining quadrature with variational approximation). Experiments in training linear binary classifiers show that the expectation-propag...

Periodic waves of the modified Korteweg-de Vries (mKdV) equation are identified in context a new variational problem with two constraints. The advantage this is that its nondegenerate local minimizers stable time evolution mKdV equation, whereas saddle points unstable. We explore analytical representation periodic given by Jacobi elliptic functions and compute numerically critical constrained p...

Abstract The Akhmediev breather (AB) and its M -breather generalisation, hereafter called AB , are exact solutions of the focusing NLS equation periodic in space exponentially localised time over constant unstable background; they describe appearance nonlinear modes their interaction, expected to play a relevant role theory anomalous (rogue) waves nature. It is therefore important establish sta...

In the limit of small activator diffusivity ε, the stability of symmetric k-spike equilibrium solutions to the Gierer-Meinhardt reaction-diffusion system in a one-dimensional spatial domain is studied for various ranges of the reaction-time constant τ ≥ 0 and the diffusivity D > 0 of the inhibitor field dynamics. A nonlocal eigenvalue problem is derived that determines the stability on an O(1) ...

We obtain multisoliton solutions of the time-dependent Bogoliubov–de Gennes equations or, equivalently, Gorkov equations that describe the dynamics of a fermionic condensate in the dissipationless regime. There are two kinds of solitons—normal and anomalous. At large times, normal multisolitons asymptote to unstable stationary states of the BCS Hamiltonian with zero order parameter normal state...

A anti-slug control requires operation around an open-loop unstable operating point. One solution is to design a robust controller based on a mechanistic model. An alternative and more robust approach is to identify an unstable model of the system based on input-output data. We used a closed-loop step test to identify an unstable linear model. From this, we obtained a second order IMC (Internal...

In this work the Gardner problem of inferring interactions and fields for an Ising neural network from given patterns under a local stability hypothesis is addressed under a dual perspective. By means of duality arguments an integer linear system is defined whose solution space is the dual of the Gardner space and whose solutions represent mutually unstable patterns. We propose and discuss Mont...