Related papers: Peakon-antipeakon interactions in the Degasperis-P…
Discrete exterior calculus (DEC) is a framework for constructing discrete versions of exterior differential calculus objects, and is widely used in computer graphics, computational topology, and discretizations of the Hodge-Laplace operator…
This paper is devoted to periodic travelling waves solving Lie-Poisson equations based on the Virasoro group. We show that the reconstruction of any such solution can be carried out exactly, regardless of the underlying Hamiltonian (which…
In this work, we show that collisions of one type of nonlinear wave can lead to generation of a different kind of nonlinear wave. Specifically, we demonstrate the formation of topological solitons (or transition waves) via collisions of…
We determine the nonlinear stability of shock-fronted travelling waves arising in a reaction-nonlinear diffusion PDE, subject to a fourth-order spatial derivative term multiplied by a small parameter $\varepsilon$ that models {\it nonlocal…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
We begin with the theoretical study of spectral energy cascade due to the propagation of high amplitude sound in the absence of thermal sources. To this end, a first-principles-based system of governing equations, correct up to second order…
We analyze the transverse-momentum spectra of strange hadrons produced in Pb+Pb collisions at the collision energy $\sqrt{s_{\rm NN}}=2.76$ TeV. Our approach combines the concept of chemical non-equilibrium with the single-freeze-out…
Recently, Dyachenko & Zakharov (2011) have derived a compact form of the well known Zakharov integro-differential equation for the third order Hamiltonian dynamics of a potential flow of an incompressible, infinitely deep fluid with a free…
Fifth-order 1D nonlinear dispersion equations are shown to admit blow-up formation of shock waves as well as rarefaction waves. The concepts of smooth deformations are applied to distinguish "entropy" shocks from smooth rarefaction waves.…
An analysis of traveling wave solutions of partial differential equation (PDE) systems with cross-diffusion is presented. The systems under study fall in a general class of the classical Keller-Segel models to describe chemotaxis. The…
The $b$-family is a one-parameter family of Hamiltonian partial differential equations of non-evolutionary type, which arises in shallow water wave theory. It admits a variety of solutions, including the celebrated peakons, which are weak…
We show that wave breaking occurs for the modified Camassa-Holm (mCH) equation. Next we classify all traveling wave solutions of the modified Camassa-Holm equation in the weak sense via parametrization of their maxima, minima and wave…
We propose a system of sine-Gordon equations, with the $\mathcal{PT}$ symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from…
Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are…
We introduce a system of Brownian particles, each absorbed upon hitting an associated moving boundary. The boundaries are determined by the conditional probabilities of the particles being absorbed before some final time horizon, given the…
Modification of optical phonon spectra in contacting nanoparticles as compared to the single ones is studied. Optical phonons in dielectric and semiconducting particles obey the Euclidean metric Klein-Fock-Gordon equation with Dirichlet…
Spontaneous symmetry breaking (SSB) and exceptional points (EPs) are often assumed to be inherently linked. Here we investigate the intricate relationship between SSB and specific classes of EPs across three distinct, real-world scenarios…
The topological presentation of pomeron exchange at the proton-proton collision of high energy is cylinder that is covered with the net of quark-gluon exchanges. I suggest that the process of double diffraction dissociation (DD) can be…
The differential equations with piecewise constant argument (DEPCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded,…
We introduce a PDE-based node-to-element contact formulation as an alternative to classical, purely geometrical formulations. It is challenging to devise solutions to nonsmooth contact problem with continuous gap using finite element…