Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with PT-symmetric potential.

Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( PT) symmetric potential for Ablowitz-Musslimani equation. And we consider the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predict the long-living rogue wave solutions. Our results might provide useful information for potential applications of synthetic PT symmetric systems in nonlinear optics and condensed matter physics.

Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation.

In this paper, the exact solutions of generalized nonlinear Schrödinger (GNLS) equation are obtained by using Darboux transformation(DT). We derive some expressions of the 1-solitons, 2-solitons and n-soliton solutions of the GNLS equation via constructing special Lax pairs. And we choose different seed solutions and solve the GNLS equation to obtain the soliton solutions, breather solutions and rational wave solutions. Based on these obtained solutions, we consider the elastic interactions and dynamics between two solitons.

Bioinspired soft robots for deep-sea exploration.

The deep ocean, Earth's untouched expanse, presents immense challenges for exploration due to its extreme pressure, temperature, and darkness. Unlike traditional marine robots that require specialized metallic vessels for protection, deep-sea species thrive without such cumbersome pressure-resistant designs. Their pressure-adaptive forms, unique propulsion methods, and advanced senses have inspired innovation in designing lightweight, compact soft machines. This perspective addresses challenges, recent strides, and design strategies for bioinspired deep-sea soft robots. Drawing from abyssal life, it explores the actuation, sensing, power, and pressure resilience of multifunctional deep-sea soft robots, offering game-changing solutions for profound exploration and operation in harsh conditions.

Some anomalous exact solutions for the four-component coupled nonlinear Schrödinger equations on complex wave backgrounds.

The coupled nonlinear Schrödinger (CNLS) equations are the important models for the study of the multicomponent Bose-Einstein condensates (BECs). In this paper, we study the four-components CNLS equations via Darboux transformation and obtain the N-soliton solutions with zero seed and non-zero seed solutions([Formula: see text] or [Formula: see text]. The 1-soliton solution and 2-soliton solution are calculated on complex wave backgrounds, the dark-bright-bright-bright soliton solutions and dark-dark-bright-bright soliton solutions are constructed. We can obtain a new class of dark-bright-bright-bright soliton solutions, which admit one-valley dark soliton in component [Formula: see text] and triple-hump bright solitons in the other three components. The collision properties between dark-dark-bright-bright solitons are considered, and the vector solitons are expected to be much more abundant than those of previously reported vector soliton collisions.

[Principal components analysis with sensation network applied in the recognition of medicine spectrum].

On the basis of classical theory about spectral analysis, the present article used the method of principal component analysis to get the specificity of 83 ultraviolet absorption spectra from mammary gland patient pathology pieces of 83 cases. The authors chose 44 principal component data as training samples and the rest 39 as testing samples. After training discrete and continual sensation network, the authors found that the recognition rate of cancer was only 43.3% and the recognition of noncancerous one was 38.7% when using the discrete sensation network However, because fuzzy-mathematics was introduced to the continual sensation network and the output value of this model was expanded to [0,1], the recognition rate of cancer reached 83.6% and that of noncancerous one was 76.3% when using this model.

Some novel soliton solution, breather solution and Darboux transformation for a generalized coupled Toda soliton hierarchy.

A few of discrete integrable coupling systems(DICSs) of previous papers are linear discrete integrable couplings(LDICS). We take a special matrix Lie algebra system(non-semisimple) to construct the Lax pairs, and establish a method for deriving the nonlinear discrete integrable coupling systems(NDICS). From the Lax pairs of the generalized Toda(G-Toda) spectral problem, we can derive a novel NDICS, which is a real NDICS. For the obtained lattice integrable coupling equation, we establish a Darboux transformation (DT) with 4 × 4 Lax pairs, and apply the gauge transformation to a specific equation, then the explicit solutions of the lattice integrable coupling equation are given, which contains discrete soliton solution, breather solution and rogue wave solution. Furthermore, we can derive the discrete explicit solutions with free parameters to depict their dynamic behaviors.

Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials.

We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.

Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.