斑图形成与孤子

We construct a novel family of exact cnoidal wave and soliton solutions of the focusing and defocusing Ablowitz-Ladik equations. Unlike cnoidal waves that were obtained by earlier authors, the phase variable of the new solutions exhibits a…

We construct a mathematical model for a diffusiophoretic motion of a deformable droplet, which is floating on a liquid surface and is driven by the surface tension gradient originating from the surface concentration field of the chemicals…

We investigate the pattern dynamics of the one-dimensional nonreciprocal Swift-Hohenberg model. Characteristic spatiotemporal patterns such as disordered, aligned, swap, chiral-swap, and chiral phases emerge depending on the parameters. We…

Nonequilibrium spatiotemporal patterns have been extensively studied. However, a single oscillator or cyclic loop of states is typically employed at each site in theories and simulations. Here, we investigate how competition among multiple…

In discrete nonlinear systems, the study of nonlinear waves has revealed intriguing phenomena in various fields such as nonlinear optics, biophysics, and condensed matter physics. Discrete nonlinear Schr\"odinger (DNLS) equations are often…

We investigate the spectral and dynamical properties of the fractional nonlinear Schr\"odinger (fNLS) equation with harmonic confinement. In this setting, the classical Laplacian is replaced by its fractional power…

Interacting rotating spiral waves have been observed in complex systems, such as cardiac fibrillation, cognitive processing in the brain cortex and oscillating chemical reactions, during dynamical regimes that are still poorly understood.…

We investigate the formation and interaction of solitons in the non-integrable Ostrovsky equation characterized by anomalous (positive) dispersion. This equation is relevant for describing wave phenomena in various media, including plasma,…

We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A…

The Korteweg-de Vries (KdV) equation governs the propagation of nonlinear internal and surface gravity waves in shallow ocean environments, where the balance between nonlinear steepening and frequency-dependent dispersion produces solitons.…

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

Adaptive coupling in networks of interacting neurons has gained recent attention due to the many applications both in biological and in artificial neural networks, where adaptive coupling or synaptic plasticity is considered as a key factor…

We study the formation of breathers in multi-dimensional lattices with long-range interactions. By variational methods, the exact relationship between various parameters (dimension, nonlinearity, nonlocal parameter $\alpha$) that defines…

In the present work we explore features of single and pairs of solitary waves in a fractional variant of the nonlinear Schr{\"o}dinger equation. Motivated by the recent experimental realization of arbitrary fractional exponents, upon…

We consider stationary states of an effectively one-dimensional Bose-Einstein condensate in a quasiperiodic lattice. We formulate sufficient conditions for a one-to-one correspondence between the stationary states with a fixed chemical…

Competition during range expansions is of great interest from both practical and theoretical view points. Experimentally, range expansions are often studied in homogeneous Petri dishes, which lack spatial anisotropy that might be present in…

This paper explores the rich structure of peakon and pseudo-peakon solutions for a class of higher-order $b$-family equations, referred to as the $J$-th $b$-family ($J$-bF) equations. We propose several conjectures concerning the weak…

We construct a new nonlinear deformed Schr\"odinger structure using a nonlinear derivative operator which depends on a parameter $q$. This operator recovers Newton derivative when $q \rightarrow 1$. Using this operator we propose a deformed…

We investigate the interplay of nonreciprocity and nonlinearity in a one-dimensional nonlinear Klein-Gordon chain of classical oscillators coupled by asymmetric springs, akin to a mechanical analogue of the Hatano-Nelson model with onsite…

In this work, we demonstrate that the synergetic interplay of topology, nonreciprocity and nonlinearity is capable of unprecedented effects. We focus on a nonreciprocal variant of the Su-Shrieffer-Heeger chain with local Kerr nonlinearity.…