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In the multiple-soliton case, the freedom in the expansion of the solution of the perturbed KdV equation is exploited so as to transform the equation into a system of two equations: The (inte-grable) Normal Form for KdV-type solitons, which…
The KdV equation is the canonical example of an integrable non-linear partial differential equation supporting multi-soliton solutions. Seeking to understand the nature of this interaction, we investigate different ways to write the KdV…
Starting from the random phase approximation for the weakly coupled multiband tightly-bounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
The nonrelativistic many-electron system in the forward, exchange and BCS approximation is considered. In this approximation, which is still quartic in the annihilation and creation operators, the model is explicitly solvable for arbitrary…
We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
We design dipolar quantum many-body Hamiltonians that will facilitate the realization of exotic quantum phases under current experimental conditions achieved for polar molecules. The main idea is to modulate both single-body potential…
Nonlinear energy transfer and dissipation in Alfv\'en wave turbulence are analyzed in the first gyrokinetic simulation spanning all scales from the tail of the MHD range to the electron gyroradius scale. For typical solar wind parameters at…
We propose multiloop vacuum amplitudes as the optimal building blocks for efficiently assembling theoretical predictions at high-energy colliders. This hypothesis is strongly supported by the manifestly causal properties of the loop-tree…
Rydberg atoms provide a powerful platform for exploring strongly interacting quantum systems, both in free space and in structured electromagnetic environments, with growing applications in quantum technology. Accurately modeling their…
The simple 3-D radiative transfer model in the atmosphere of the Earth is built for numerical comparison of direct solar radiation and limb scattering background at the definite layer during the deep twilight period at the middle and upper…
Complementing a study which was published in this journal in 2005, we present explicit calculations of fields predicted by Maxwell's equations both in Lorenz and in Coulomb gauge. Analytic expressions are obtainable, when the source of the…
Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous…
Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…
Diffraction of multi-level atoms by an evanescent wave reflective diffraction grating is modeled by numerically solving the time-dependent Schr\"{o}dinger equation. We are able to explain the diffraction observed in experiments with…
In this paper, a variable coefficient Bilinear neural network method is proposed to deal with the analytical solutions of variable coefficient nonlinear partial differential equations. As an example, a Kadomstev-Petviashvili equation with…
The role of multiple soliton and breather interactions in formation of very high waves is disclosed within the framework of integrable modified Korteweg - de Vries (mKdV) equation. Optimal conditions for the focusing of many solitons are…
In theoretical models of tropical dynamics, the effects of both surface friction and upward wave radiation through interaction with the stratosphere are oft-ignored, as they greatly complicate mathematical analysis. In this study, we relax…
We show that nonradiative interactions between atomic dipoles placed in a waveguide can give rise to deterministic entanglement at ranges much larger than their resonant wavelength. The range increases as the dipole-resonance approaches the…