The fractional nonlinear Schrödinger equation: Soliton turbulence, modulation instability, and extreme rogue waves.

In this paper, we undertake a systematic exploration of soliton turbulent phenomena and the emergence of extreme rogue waves within the framework of the one-dimensional fractional nonlinear Schrödinger (FNLS) equation, which appears in many fields, such as nonlinear optics, Bose-Einstein condensates, plasma physics, etc. By initiating simulations with a plane wave modulated by small noise, we scrutinized the universal regimes of non-stationary turbulence through various statistical indices. Our analysis elucidates a marked increase in the probability of rogue wave occurrences as the system evolves within a certain range of Lévy index α, which can be ascribed to the broadened modulation instability bandwidth.

Large-space and large-time asymptotic properties of vector rogon-soliton and soliton-like solutions for n-component NLS equations.

In this paper, we analyze the large-space and large-time asymptotic properties of the vector rogon-soliton and soliton-like solutions of the n-component nonlinear Schrödinger equation with mixed nonzero and zero boundary conditions. In particular, we find that these solutions have different decay velocities along different directions of the x axis, that is, the solutions exponentially and algebraically decay along the positive and negative directions of the x axis, respectively. Moreover, we study the change of the acceleration of soliton moving with the increase in time or distance along the characteristic line (i.

Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations.

In this paper, using the algorithm due to Ablowitz et al. [Phys. Rev.

[Study on the prevalence of arthritis and relevant factors in Shanghai].

Objective: This study aimed to understand the prevalence rate, epidemiological characteristics and relevant factors of arthritis in Shanghai.

Methods: A sample of 7 575 residents aged 15 years and above was drawn from 6 communities under multiple stage cluster sampling. A household survey with questionnaire was carried out to differentiate both undiagnosed patients and those with definite arthritis.