### Effective stochastic model for chaos in the Fermi-Pasta-Ulam-Tsingou chain

Understanding the interplay between different wave excitations, such as phonons, localized solitons, and chaotic breathers, is crucial for developing coarse-grained descriptions of many-body, near-integrable systems. We treat the Fermi-Pasta-Ulam-Tsingou (FPUT) non-linear chain and show numerically that at short timescales, relevant to the maximal Lyapunov exponent, it can be modeled as a random perturbation of its integrable approximation -- the Toda chain. At low energies, the Lyapunov separation is dictated by the interaction between few soliton modes and an intrinsic, apparent bath representing a background of many radiative modes. It is sufficient to consider only one randomly perturbed Toda soliton-like mode to explain the anomalous power-laws reported in previous works, describing how the Lyapunov exponent of large FPUT chains decreases with the energy density of the system.

### Stability analysis of generalized Lugiato-Lefever equation with lumped filter for Kerr optical soliton generation in anomalous dispersion regime

We raise a detuning-dependent loss mechanism to describe the soliton formation dynamics when the lumped filtering operation is manipulated in anomalous group velocity dispersion regime, using stability analysis of generalized Lugiato-Lefever equation.

### Moving efficiently through a crowd: a nature inspired traffic rule

In this article, we propose a traffic rule inspired from nature, that facilitates an elite agent to move efficiently through a crowd of inert agents. When an object swims in a fluid medium or an intruder is forced through granular matter, characteristic flow-fields are created around them. We show that if inert agents, made small movements based on a traffic rule derived from these characteristic flow-fields, they efficiently reorganize and transport enough space for the elite to pass through. The traffic rule used in the article is a dipole-field which satisfactorily captures the features of the flow-fields around a moving intruder. We study the effectiveness of this dipole traffic rule using numerical simulations in a 2D periodic domain, where one self-propelled elite agent tries to move through a crowd of inert agents that prefer to stay in a state of rest. Simulations are carried out for a wide range of strengths of the traffic rule and packing density of the crowd. We characterize and analyze four regions in the parameter space, free-flow, motion due to cooperation, frozen and collective drift regions, and discuss the consequence of the traffic rule in light of the collective behavior observed. We believe that the proposed method can be of use in a swarm of robots working in constrained environments.

### Non-Hermitian singularities induced single-mode depletion and soliton formation in microresonators

On-chip manipulation of single resonance over broad background comb spectra of microring resonators is indispensable, ranging from tailoring laser emission, optical signal processing to non-classical light generation, yet challenging without scarifying the quality factor or inducing additional dispersive effects. Here, we propose an experimentally feasible platform to realize on-chip selective depletion of single resonance in microring with decoupled dispersion and dissipation, which are usually entangled by Kramer-Kroning relation. Thanks to the existence of non-Hermitian singularity, unsplit but significantly increased dissipation of the selected resonance is achieved due to the simultaneous collapse of eigenvalues and eigenvectors, fitting elegantly the requirement of pure single-mode depletion. With delicate yet experimentally feasible parameters, we show explicit evidence of modulation instability as well as deterministic single soliton generation in microresonators induced by depletion in normal and anomalous dispersion regime, respectively. Our findings connect non-Hermitian singularities to wide range of applications associated with selective single mode manipulation in microwave photonics, quantum optics, ultrafast optics and beyond.

### Existence of localised radial patterns in a model for dryland vegetation

Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of `fairy circles'. We consider stationary localised radial solutions to a reduced model for dryland vegetation on flat terrain. By considering certain prototypical pattern-forming systems, we prove the existence of three classes of localised radial patterns bifurcating from a Turing instability. We also present evidence for the existence of localised gap solutions close to a homogeneous instability. Additionally, we numerically solve the vegetation model and explore the bifurcation structure and stability of localised radial spots and gaps. We conclude by investigating the effect of varying certain parameter values on the existence and stability of these localised radial patterns.

### Lie symmetry structure of nonlinear wave equations

We study Lie point symmetry structure of generalized nonlinear wave equations in the $1+n$-dimensional space-time.