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Basic problems of the semiclassical microscopic modelling of strongly interactingsystems are discussed within the framework of Quantum Molecular Dynamics (QMD). This model allows to study the influence of several types of nucleonic…
Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector…
We describe an approach to construct multi-soliton asymptotic solutions for non-integrable equations. The general idea is realized in the case of three waves and for the KdV-type equation with nonlinearity $u^4$. A brief review of…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
The KdV equation is a model equation for waves at the surface of an inviscid incompressible fluid, and it is well known that the equation describes the evolution of unidirectional waves of small amplitude and long wavelength fairly…
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…
Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated . Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are…
The susceptibility of timestepping algorithms to numerical instabilities is an important consideration when simulating partial differential equations (PDEs). Here we identify and analyze a pernicious numerical instability arising in…
The latest molecular data - potential energy curves and Rydberg$/$valence interactions - characterizing the super-excited electronic states of CO are reviewed, in order to provide inputs for the study of their fragmentation dynamics.…
A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface…
In this paper, we begin with extended Majda--Biello system (BSAB equations): $$ \left\{\begin{array}{l} 0=A_t-DA_3+\mu A_1+\Gamma_S B^S_1+\Gamma_A B_1^A+\left(AB^S\right)_x \\ 0=B^S_t-B_3^S+\Gamma_SA_1+\lambda B_1^S+\sigma B^A_1+AA_1 \\…
This paper is concerned with the study of the main wave interactions in a system of conservation laws in geochemical modeling. We study the modeling of the chemical complexes on the rock surface. The presence of stable surface complexes…
Van der Waals interactions are ubiquitous and they play an important role for the stability of materials. Current understanding of this type of coupling is based on linear response theory, while optical nonlinearities are rarely considered…
Quantum-mechanical methods are widely used for understanding molecular interactions throughout biology, chemistry, and materials science. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple…
High harmonic generation in solids provides us compact and coherent UV sources. Our simulations illustrate abnormal harmonic yield dependence on the intensity of driving or pre-excitation pulses. A multielectron interference model is…
Ideal MHD provides an accurate description of low-frequency Alfv\'en waves in fully ionized plasmas. However, higher frequency waves in many plasmas of the solar atmosphere cannot be correctly described by ideal MHD and a more accurate…
Compactons are studied in the framework of the Korteweg-de Vries (KdV) equation with the sublinear nonlinearity. Compactons represent localized bell-shaped waves of either polarity which propagate to the same direction as waves of the…
The three-wave resonant interaction equations are a non-dispersive system of partial differential equations with quadratic coupling describing the time evolution of the complex amplitudes of three resonant wave modes. Collisions of wave…
In this paper we derive a higher-order KdV equation (HKdV) as a model to describe the unidirectional propagation of waves on an internal interface separating two fluid layers of varying densities. Our model incorporates underlying currents…
Analysis of satellite altimetry and Argo float data leads Ni et al. (2020, JGR Oceans) to argue that mesoscale dipoles are widespread features of the global ocean having a relatively uniform three-dimensional structure that can lead to…