斑图形成与孤子
We introduce a novel neural network structure called Strongly Constrained Theory-Guided Neural Network (SCTgNN), to investigate the behaviours of the localized solutions of the generalized nonlinear Schr\"{o}dinger (NLS) equation. This…
We study nonlocal bright solitons subject to external spatially nonuniform potentials. If the potential is slowly varying on the soliton scale, we derive analytical soliton solutions behaving like Newtonian particles. If the potential has…
We study the fractional three-dimensional (3D) nonlinear Schr\"{o}dinger equation with exponential saturating nonlinearity. In the case of the L\'{e}vy index $\alpha=1.9$, this equation can be considered as a model equation to describe…
The Ivancevic option pricing model is studied via variational approach. Both the Gaussian anstz and the (sech ansatz are used, and each has a unique results from one another. But in terms of existance of soliton solutions they both agree…
Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics…
We study dynamics of dark solitons in the theory of the DNLS equation by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes' remark that relationships for harmonic linear…
We suggest the method of derivation of Hamilton equations which describe the motion of solitons along non-uniform and time dependent large-scale background in case of wave dynamics described by the completely integrable equations in the…
Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give…
We present an experimental study on the perturbed evolution of Korteweg-deVries soliton gases in a weakly dissipative nonlinear electrical transmission line. The system's dynamics reveal that an initially dense, fully randomized, soliton…
Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to…
The Heimburg-Jackson model, or thermodynamic soliton theory of nervous impulses, has a well-established record as an alternative model for studying the dynamics of nerve impulses and lipid bilayers. Within this framework, nerve impulses can…
The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary…
Here, I derive an Ising Hamiltonian for $N$ coupled fibre-based Optical Parametric Oscillators (OPOs). For this, I use the Lugiato-Lefever equation. The derivation of the Hamiltonian does not pretend to be mathematically correct, although…
A fully coupled network of Mackey-Glass generators is considered. Each generator is described by a limit equation for the Mackey-Glass equation. The right parts are represented by a relay function obtained when the exponent in the…
We studied discrete transmission lines constructed from ideal linear inductors and nonlinear capacitors (and possibly resistors). The localised travelling waves in the lossless transmission lines are the kinks and the solitons, which speeds…
We consider the series-connected Josephson transmission line (JTL), constructed from Josephson junctions, capacitors and (possibly) resistors. We calculate the velocity of shocks in the discrete lossy JTL. We study thoroughly the continuum…
We consider the modulated harmonic wave in the discrete series connected Josephson transmission line (JTL). We formulate the approach to the modulation problems for discrete wave equations based on discrete calculus. We check up the…
We study the dynamics of fundamental and vortex solitons in the framework of the nonlinear Schr\"{o}dinger equation with the spatial dimension $D\geqslant 2$ with a multiplicative random term depending on the time and space coordinates. To…
We argue that the spatial discretization of the strongly nonlinear Lefever-Lejeune partial differential equation defines a nonlinear lattice that is physically relevant in the context of the nonlinear physics of ecosystems, modelling the…
The influence of Gilbert damping on the propagation of electromagnetic waves (EMWs) in an anisotropic ferromagnetic medium is investigated theoretically. The interaction of the magnetic field component of the electromagnetic wave with the…