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We present a multichannel model for elastic interactions, comprised of an arbitrary number of coupled finite square-well potentials, and derive semi-analytic solutions for its scattering behavior. Despite the model's simplicity, it is…
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…
The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging…
We demonstrate a scaling method for non-Markovian Monte Carlo wave-function simulations used to study open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values…
The standard DLVO theory offers a limited description of ionic-surfacted magnetic colloids in near aggregation regimes. Correcting the electrical double layer term for ionic surfactants is not enough to successfully simulate the systems.…
We present the discovery of a class of exact spatially localized as well as periodic wave solutions within the framework of the modified Korteweg-de Vries equation. This class comprises breather and interacting soliton solutions as well as…
This work constructs an advanced force field, the Completely Multipolar Model (CMM), to quantitatively reproduce each term of an energy decomposition analysis (EDA) for aqueous solvated alkali metal cations and halide anions and their ion…
Three-dimensional equatorial trapped waves excited by stellar isolation and the resulting equatorial superrotating jet in a vertical stratified atmosphere of a tidally-locked hot Jupiter are investigated. Taking the hot Jupiter HD 189733b…
The multiple scattering of scalar waves in diffusive media is investigated by means of the radiative transfer equation. This approach amounts to a resummation of the ladder diagrams of the Born series; it does not rely on the diffusion…
We derive a new set of kinematic equations for front motion in two-dimensional bistable media. The equations generalize the geometric approach by complementing the equation for the front curvature with an order parameter equation associated…
Nonlinear waves in dispersive media can be succeptible to modulational instabilities. We examine a category of scalar equations, with general dispersion and monomial nonlinearity, including a large variety of KdV-like equations. For…
The Darboux transformation of the three-component coupled derivative nonlinear Schr\"{o}dinger equations is constructed, based on the special vector solution elaborately generated from the corresponding Lax pair, various interactions of…
Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…
The coupled-mode theory is developed for description of the nonlinear wave dynamics in binary optical lattices. The obtained equations of motion accurately describe nonlinear wave dynamics close to the band edges and in the gap of the…
We study the parameter space of cnoidal waves -- the periodic solitons of the Korteweg-de Vries equation -- from the perspective of Virasoro coadjoint orbits. The monodromy method familiar from inverse scattering implies that many, but not…
The onset of collision dynamics between an ion and a Rydberg atom is studied in a regime characterized by a multitude of collision channels. These channels arise from coupling between a non-polar Rydberg state and numerous highly polar…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
In this paper we study dispersive wave equation using the method of multiple scales (MMS) and perform several numerical tests to investigate its accuracy. The key feature of our MMS solution is the linearity of the amplitude equation and…
Whether monochromatic, pulsed, or even constant and crossed, the field used to describe the interaction of charged fermions with an intense laser beam is mainly assumed to be of plane-wave form. We consider a simple extension to plane-wave…
The universal scaling behavior for the electron-impact excitation cross sections of the $2s$ states of hydrogen- and helium-like multicharged ions is deduced. The study is performed within the framework of non-relativistic perturbation…