Related papers: General real-valued theories with the Schr\"oder-B…
In this paper, we prove the energy stable property for time-dependent (generalized) Schr\"{o}dinger operators by using Hardy inequality. Such property acts very important roles in quantum scattering theory and nonlinear problem. As an…
We consider the complex Ginzburg-Landau equation with two pure-power nonlinearities and a damping term. After proving a general global existence result, we focus on the existence and stability of several periodic orbits, namely the trivial…
We study stable like behaviour in first order theories without the independence property. We introduce generically stable measures, give characterizatiions, and show their ubiquity. We also introduce generic compact domination. We also…
We prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi stating that the validity of Bernstein's theorem in dimension $n+1$ is a consequence of…
Generalized relational theories with null values in the sense of Reiter are first-order theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an…
The higher derivative field theories are notorious for the stability problems both at classical and quantum level. Classical instability is connected with unboundedness of the canonical energy, while the unbounded energy spectrum leads to…
We generalize Hrushovski's group configuration theorem to the case where the type of the configuration is generically stable, without assuming tameness of the ambient theory. The properties of generically stable types, which we recall in…
We generalize the stable graph regularity lemma of Malliaris and Shelah to the case of finite structures in finite relational languages, e.g., finite hypergraphs. We show that under the model-theoretic assumption of stability, such a…
This paper is concerned with controllability and stabilization properties of the dispersion generalized Benjamin equation on the periodic domain $\mathbb{T}.$ First, by assuming the control input acts on all the domain, the system is proved…
We study the stability of the one electron atom Schr\"odinger model with self-generated magnetic field in two dimensions. The magnetic energy is taken of the general form $K\int_{\mathbb{R}^2} |B|^p$ and we study the stability of the model…
We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing $\hbar$ to be a function of the momentum or wave vector rather than a…
We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all…
The stability criteria for the generalized Brans-Dicke cosmology in a spatially flat, homogeneous and isotropic cosmological model is discussed in the presence of a perfect fluid. The generalization comes through the channel that the…
We show that generalized coherent states follow Schr\"{o}dinger dynamics in time-dependent potentials. The normalized wave-packets follow a classical evolution without spreading; in turn, the Schr\"{o}dinger potential depends on the state…
We consider numerical instability that can be observed in simulations of localized solutions of the generalized nonlinear Schr\"odinger equation (NLS) by a split-step method where the linear part of the evolution is solved by a…
Stimulated by the category theorems of Eisner and Ser\'eny in the setting of unitary and isometric $C_0$-semigroups on separable Hilbert spaces, we prove category theorems for Schr\"odinger semigroups. Specifically, we show that, to a given…
We introduce and study the notion of conic stability of multivariate complex polynomials in $\mathbb{C}[z_1,\ldots, z_n]$, which naturally generalizes the stability of multivariate polynomials. In particular, we generalize Borcea's and…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
The Markov-Bernstein type inequalities between the norms of functions and of their derivatives are analysed for complex exponential polynomials. We establish a relation between the sharp constants in those inequalities and the stability…
We consider the one dimensional Schr\"odinger equation with a bilinear control and prove the rapid stabilization of the linearized equation around the ground state. The feedback law ensuring the rapid stabilization is obtained using a…