Nonlinear waves in coherently coupled Bose-Einstein condensates

We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the elementary excitations. The spectrum has two branches which are affected in different ways. The upper branch experiences a modulational instability which is stabilized by a long wave-short wave resonance with the lower branch. The lower branch is stable. In the limit of weak nonlinearity and small dispersion it is described by a Korteweg-de Vries equation or by the Gardner equation, depending on the value of the parameters of the system

Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

We provide a classification of the possible flow of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferro-magnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as to the appearance of new elements --- contact dispersive shock waves --- that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations

Statistics of extreme events in integrable turbulence

We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schr\"odinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result to two fundamental scenarios of the generation of integrable turbulence: (i) the asymptotic development of the spontaneous (noise induced) modulational instability of a plane wave, and (ii) the long-time evolution of strongly nonlinear, partially coherent waves. In both cases, involving the bound state soliton gas dynamics, the analytically obtained values of the kurtosis are in perfect agreement with those inferred from direct numerical simulations of the the fNLSE, providing the long-awaited theoretical explanation of the respective rogue wave statistics. Additionally, the evolution of a particular non-bound state gas is considered providing important insights related to the validity of the so-called virial theorem.Comment: 11 pages, 5 figure

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations

A single amino acid distorts the Fc γ receptor IIIb/CD16b structure upon binding immunoglobulin G1 and reduces affinity relative to CD16a

Therapeutic mAbs engage Fc γ receptor III (CD16) to elicit a protective cell-mediated response and destroy the target tissue. Newer drugs designed to bind CD16a with increased affinity surprisingly also elicit protective CD16b-mediated responses. However, it is unclear why IgG binds CD16a with more than 10-fold higher affinity than CD16b even though these receptors share more than 97% identity. Here we identified one residue, Gly-129, that contributes to the greater IgG binding affinity of CD16a. The CD16b variant D129G bound IgG1 Fc with 2-fold higher affinity than CD16a and with 90-fold higher affinity than the WT. Conversely, the binding affinity of CD16a-G129D was decreased 128-fold relative to WT CD16a and comparably to that of WT CD16b. The interaction of IgG1 Fc with CD16a, but not with CD16b, is known to be sensitive to the composition of the asparagine-linked carbohydrates (N-glycans) attached to the receptor. CD16a and CD16b-D129G displaying minimally processed oligomannose N-glycans bound to IgG1 Fc with about 5.2-fold increased affinity compared with variants with highly processed complex-type N-glycans. CD16b and the CD16a-G129D variant exhibited a smaller 1.9-fold affinity increase with oligomannose N-glycans. A model of glycosylated CD16b bound to IgG1 Fc determined to 2.2 Å resolution combined with a 250-ns all-atom molecular dynamics simulation showed that the larger Asp-129 residue deformed the Fc-binding surface. These results reveal how Asp-129 in CD16b affects its binding affinity for IgG1 Fc and suggest that antibodies engineered to engage CD16b with high affinity must accommodate the Asp-129 side chain

Dispersive hydrodynamics of nonlinear polarization waves in two-component Bose-Einstein condensates

We study one dimensional mixtures of two-component Bose-Einstein condensates in the limit where the intra-species and inter-species interaction constants are very close. Near the mixing-demixing transition the polarization and the density dynamics decouple. We study the nonlinear polarization waves, show that they obey a universal (i.e., parameter free) dynamical description, identify a new type of algebraic soliton, explicitly write simple wave solutions, and study the Gurevich-Pitaevskii problem in this context