Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation \({\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial _x^2u + u{u_x} = 0\), where \({\cal H}\) denotes the Hilbert transform operator. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \({\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)\), which is a subspace of L²(ℝ). It is worth noting that the low-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is scaling critical, and thus the small data is necessary. The high-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is equal to the Sobolev space H^σ (ℝ) (σ ⩾ 0) and reduces to L²(ℝ). Furthermore, we also obtain its inviscid limit behavior in \({\tilde H^\sigma }(\mathbb{R})\) (σ ⩾ 0).

     

Semi-invariants of binary forms and Sylvester’s theorem

The Ramanujan Journal - We obtain a combinatorial formula related to the shear transformation for semi-invariants of binary forms, which implies the classical characterization of semi-invariants in...     

Portfolio Selection and Risk Control for an Insurer With Uncertain Time Horizon and Partial Information in an Anticipating Environment

Methodology and Computing in Applied Probability - This paper is devoted to the study of an optimal investment and risk control problem for an insurer. The risky asset process and the insurance...     

Multistable dynamics in a Hopfield neural network under electromagnetic radiation and dual bias currents

Nonlinear Dynamics - This paper investigates a Hopfield neural network under the simulation of external electromagnetic radiation and dual bias currents, in which the fluctuation of magnetic flux...     

Asymmetric nonlinear-mode-conversion in an optical waveguide withPT symmetry

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.     

Preparation of LiNi0.5Mn1.5O4 cathode materials by using different-sized Mn3O4 nanocrystals as precursors

Journal of Solid State Electrochemistry - High-voltage LiNi0.5Mn1.5O4 with a spinel structure is considered as important cathode materials for high-energy density Li-ion batteries (LIBs). In this...     

Asymptotics of Smoothed Wasserstein Distances

Potential Analysis - We investigate contraction of the Wasserstein distances on $\mathbb {R}^{d}$ under Gaussian smoothing. It is well known that the heat semigroup is exponentially contractive...     

Collisional dynamics of symmetric two-dimensional quantum droplets

The collisional dynamics of two symmetric droplets with equal intraspecies scattering lengths and particle number density for each component is studied by solving the corresponding extended Gross−Pitaevskii equation in two dimensions by including a logarithmic correction term in the usual contact interaction. We find the merging droplet after collision experiences a quadrupole oscillation in its shape and the oscillation period is found to be independent of the incidental momentum for small droplets. With increasing collision momentum the colliding droplets may separate into two, or even more, and finally into small pieces of droplets. For these dynamical phases we manage to present boundaries determined by the remnant particle number in the central area and the damped oscillation of the quadrupole mode. A stability peak for the existence of droplets emerges at the critical particle numberN_c ≃ 48 for the quasi-Gaussian and flat-top shapes of the droplets.