Modulational instability, higher-order localized wave structures, and nonlinear wave interactions for a nonautonomous Lenells-Fokas equation in inhomogeneous fibers.

In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated. The modulational instability analysis of the solutions with variable coefficients in the presence of a small perturbation is studied. Higher-order soliton, breather, earthwormon, and rogue wave solutions of the nonautonomous LF model are derived via the n-fold variable-coefficient Darboux transformation. The solitons and earthwormons display the elastic collisions. It is found that the nonautonomous LF model admits the higher-order periodic rogue waves, composite rogue waves (rogue wave pair), and oscillating rogue waves, whose dynamics can be controlled by the inhomogeneous nonlinear parameters. Based on the second-order rogue wave, a diamond structure consisting of four first-order rogue waves is observed. In addition, the semirational solutions (the mixed rational-exponential solutions) of the nonautonomous LF model are obtained, which can be used to describe the interactions between the rogue waves and breathers. Our results could be helpful for the design of experiments in the optical fiber communications.

Ethnobotanical survey of medicinal plants in Gaomi, China.

ETHNOPHARMACOLOGICAL RELEVANCE: The uses of medicinal plants have a long history and become one of the important sources of the health cares in Gaomi City, Shandong Province, China. However, limited studies have been done to identify these medicinal plant species and to scientifically document their associated traditional knowledge. Many species used by indigenous people could potentially represent a novel resource of medicine. The study can aid in further investigations of modern pharmacology and planning of the wild species conservation. AIM OF THE STUDY: The study aimed to investigate and record the medicinal plant taxa and their associated traditional knowledge in Gaomi City, China. MATERIALS AND METHODS: Field study was conducted from March 2018 to May 2019 with 184 residents of Gaomi City. Traditional medicinal plant specimens were collected from the field with the help of these residents and were identified and authenticated in the Herbarium of the School of Pharmacy, Binzhou Medical University. Ethnobotanical knowledge was collected by semi-structured face-to-face interviews. The quantitative data were analyzed by using the informant consensus factor (ICF) method and the number of citations. RESULTS: A total of 181 species belonging to 137 genera and 65 families were collected in Gaomi City. Asteraceae was the predominant family and Fabaceae took the second place. River basins and the southern hills in Gaomi were rich in vegetation. However, the cultivated area of medicinal plants only accounted for 10% of agricultural acreage. The main preparation method was decocting (170, 94.48%) and the most frequent mode of administration was oral (177, 97.97%). The highest numerical ICF value was recorded for treating endocrine, metabolic, and nutritional (ICF: 0.85) conditions. Seven of the medicinal plant species used by the people in Gaomi have not been reported previously in China. Verbena officinalis L. was found in Gaomi City, which is a new distribution record for this species. CONCLUSIONS: People in Gaomi hold valuable knowledge about the use of medicinal plants; however, their knowledge has not been comprehensively documented. The therapeutic uses of the documented medicinal plants will provide a basis for further pharmacological and phytochemical investigations. Additionally, the result of this study indicated that the elder people in Gaomi have more traditional knowledge of plant medicines than the younger ones.

Breather transition dynamics, Peregrine combs and walls, and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects.

We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W-shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W-shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.

Breather-to-soliton transitions, nonlinear wave interactions, and modulational instability in a higher-order generalized nonlinear Schrödinger equation.

We study the nonlinear waves on constant backgrounds of the higher-order generalized nonlinear Schrödinger (HGNLS) equation describing the propagation of ultrashort optical pulse in optical fibers. We derive the breather, rogue wave, and semirational solutions of the HGNLS equation. Our results show that these three types of solutions can be converted into the nonpulsating soliton solutions. In particular, we present the explicit conditions for the transitions between breathers and solitons with different structures. Further, we investigate the characteristics of the collisions between the soliton and breathers. Especially, based on the semirational solutions of the HGNLS equation, we display the novel interactions between the rogue waves and other nonlinear waves. In addition, we reveal the explicit relation between the transition and the distribution characteristics of the modulation instability growth rate.