斑图形成与孤子

We present results of the application of the numerical continuation and bifurcation package pde2path to the 3D Brusselator model, focusing on snaking branches of planar fronts between body centered cubes (BCCs) and the spatial homogeneous…

In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these…

In this work, we develop an analytical framework to explain the influence of dissipation and detuning parameters on the emergence and stability of autoresonance in a strongly nonlinear weakly damped chain subjected to harmonic forcing with…

This thesis deals with mathematical and physical aspects of deterministic freak wave generation in a hydrodynamic laboratory. We adopt the nonlinear Schr\"odinger (NLS) equation as a mathematical model for the evolution of the surface…

We visualize the Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in a classical Heisenberg ferromagnetic (HF) spin chain by exploiting its gauge eq uivalence to the nonlinear Schr\"{o}dinger equation (NLSE). We discuss two types of spatially…

The stability and dynamical properties of the so-called resonant nonlinear Schr\"odinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear Schr\"odinger (NLS) equation with the addition of a perturbation used to…

We develop the theoretical procedures for shifting the frequency of a single soliton and of a sequence of solitons of the nonlinear Schr\"odinger equation. The procedures are based on simple transformations of the soliton pattern in the…

We study the dynamics of emission of radiation (small-amplitude waves) in fast collisions between two solitons of the nonlinear Schr\"odinger (NLS) equation in the presence of weak cubic loss. We calculate the radiation dynamics by a…

Hydrodynamic instabilities often cause spatio-temporal pattern formations and transitions between them. We investigate a model experimental system, a density oscillator, where the bifurcation from a resting state to an oscillatory state is…

Excitable pulses are among the most widespread dynamical patterns that occur in many different systems, ranging from biological cells to chemical reactions and ecological populations. Traditionally, the mutual annihilation of two colliding…

Post-earthquake damage evaluation has indicated that although the buildings with shear walls exhibited an appropriate overall performance in the recent severe earthquakes, in some cases, however, the columns and the shear walls were…

We investigate the generation and propagation of solitary waves in the context of the Hertz chain and Toda lattice, with the aim to highlight the similarities, as well as differences between these systems. We begin by discussing the kinetic…

In this study we examine the energy transfer mechanism during the nonlinear stage of the Modulational Instability (MI) in the modified Korteweg-de Vries equation. The particularity of this study consists in considering the problem…

We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. We use…

We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes…

The collective behaviour of soliton ensembles (i.e. the solitonic gas) is studied using the methods of the direct numerical simulation. Traditionally this problem was addressed in the context of integrable models such as the celebrated KdV…

We demonstrate that the commonly known concept, which treats solitons as nonsingular solutions produced by the interplay of nonlinear self-attraction and linear dispersion, may be extended to include modes with a relatively weak singularity…

Nonuniform spatial distributions of vegetation in scarce environments consist of either gaps, bands often called tiger bush or patches that can be either self-organized or spatially localized in space. When the level of aridity is…

The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter $\kappa$ is analyzed, when the external force is periodic in space and given by $f(x) =r\cos(K x)$, both numerically and in a variational…

Reduction of a two-component FitzHugh-Nagumo model to a single-component model with long-range connection is considered on general networks. The reduced model describes a single chemical species reacting on the nodes and diffusing across…