Related papers: Gurevich-Zybin system
A reconstruction of modified gravity is proposed by establishing a correspondence between the effective density of the modified gravity and the holographic density. The non-homogeneous term in the modified Friedmann equation, generated by…
We investigate a general system of two coupled harmonic oscillators with cubic nonlinearity. Without damping, the system is Hamiltonian, with the origin as an elliptic equilibrium characterized by two distinct linear frequencies. To…
We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler-Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component…
We extend image scanning microscopy to second harmonic generation (SHG) by extracting the complex field amplitude of the second-harmonic beam. While the theory behind coherent image scanning microscopy (ISM) is known, an experimental…
We show how a symmetry reduction of the equations for incompressible hydrodynamics in three dimensions leads naturally to a Monge-Amp\`ere structure, and Burgers'-type vortices are a canonical class of solutions associated with this…
We derive a Magnus expansion for a frequency chirped quantum two-level system. We obtain a time-independent effective Hamiltonian which generates a stroboscopic time evolution. At lowest order the according dynamics is identical to results…
Second-harmonic generation (SHG) is a direct measure of the strength of second-order nonlinear optical effects, which also include frequency mixing and parametric oscillations. Natural and artificial materials with broken…
A least-squares method for solving the hyperbolic Monge-Amp\`ere equation with transport boundary condition is introduced. The method relies on an iterative procedure for the gradient of the solution, the so-called mapping. By formulating…
Integrated thin-film lithium niobate platform has recently emerged as a promising candidate for next-generation, high-efficiency wavelength conversion systems that allow dense packaging and mass-production. Here we demonstrate efficient,…
Decoherent transport in mesoscopic and nanoscopic systems can be formulated in terms of the D'Amato-Pastawski (DP) model. This generalizes the Landauer-B\"{u}ttiker picture by considering a distribution of local decoherent processes.…
We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a…
We report an unexpected systematic degeneracy between different multiplets in an inversion symmetric system of two coupled Gaudin models with homogeneous couplings, as occurring for example in the context of solid state quantum information…
There has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a…
We introduce what we call the second-order Boltzmann-Gibbs principle, which allows to replace local functionals of a conservative, one-dimensional stochastic process by a possibly nonlinear function of the conserved quantity. This…
There is a growing attention given to utilizing Lagrangian and Hamiltonian mechanics with network training in order to incorporate physics into the network. Most commonly, conservative systems are modeled, in which there are no frictional…
The plasmon-enhanced second harmonic generation in the subwavelength neutral metal cubic nanoparticles is calculated for the first time in the hydrodynamic and cold plasma approximations. The theory is developed that takes into account all…
The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary…
We consider a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of…
The well-known phase structure of the two-dimensional sine-Gordon model is reconstructed by means of its renormalization group flow, the study of the sensitivity of the dynamics on microscopic parameters. Such an analysis resolves the…
Within the framework of Lagrangian variables, we develop a method for deriving explicit solutions to the 2D Boussinesq equations using harmonic mapping theory. By reformulating the characterization of flow solutions described by harmonic…