Effects of nonlinear wave coupling: Accelerated solitons

The laser-excited, jet-cooled A 2E"-X 2E' electronic spectrum of the silver trimer yields detailed information about its A- and X-state vibronic structure. Following extensive parameter fitting, the absorption and emission spectra are simulated and the bands are assigned. The Jahn-Teller analysis includes both linear and quadratic coupling terms, considered simultaneously with spin-orbit coupling. The spin-orbit splitting is shown to be largely quenched in both the A and X electronic states. The Jahn-Teller analysis of the A and X vibronic structures reveals the distortion of their corresponding potential energy surfaces.

A multiple-scales method is used to derive the Three-Wave Interaction (TWI) equations describing resonantly interacting triads in nonlinear hyper-elastic fluid-filled tubes. The tube wall is assumed to be an axially-tethered nonlinear membraneous cylindrical shell for which the resultant stresses can be determined by a strain-energy functional. The fluid within the tube is assumed to be two-dimensional, axi-symmetric and inviscid. We show that small-but-finite amplitude strongly dispersive pressure wave packets can continuously exchange energy in a resonant triad while conserving total energy. For a Mooney-Rivlin shell wall the theory presented predicts a short wavelength cutoff on the order of the tube radius. Thus pressure pulses containing wavelengths on the order of the tube radius and longer may contain resonantly interacting modes. Special solutions are presented: temporally developing modes, pump-wave approximations and explosively unstable steadily-traveling wave packets.

Hamiltonian chaos in two coupled three-wave parametric interactions with quadratic nonlinearity

<p>Magnetohydrodynamic waves in a stratified rotating plasma in a gravitational field in the Boussinesq approximation are studied. The theory of flows on the f -plane, on the non-traditional f-plane (taking into account the horizontal component of the Coriolis force), on the beta -plane, and on the non-traditional beta -plane is developed. In each considered case linear solutions of systems of three-dimensional magnetohydrodynamic equations in the Boussinesq approximation are obtained in form of magnetic inertio-gravity waves, magnetostrophic waves, and magneto-Rossby waves. For equations of a rotating stratified plasma without taking into account sphericity (in the approximation of the f-plane and the non-traditional f- plane), dispersion relations describe three-dimensional magnetic inertio-gravity waves and three-dimensional magnetostrophic waves. In the case of propagating only along the vertical component of the wave vector, their dispersion relations describe two types of magnetic waves, the first of which is a special case of magnetic inerto-gravity waves propagating only vertically, and the second is a special case of magnetostrophic waves propagating only vertically. In addition, it was found that dispersion relations describing wave propagation taking into account sphericity in a first approximation (on the beta-plane and on the non-traditional beta- plane) along the vertical component of the wave vector have a similar particular form. In the case of wave propagation in a horizontal plane, magnetic inertio-gravity waves turn into Alfvén waves, and magnetostrophic waves turn into magnetogravitational waves. In addition, for waves on a non-traditional f-plane, the influence of the horizontal component of the Coriolis force on the existence of various types of three-wave interactions is shown. For equations of a rotating stratified plasma on the beta-plane and on the non-traditional beta-plane dispersion relations for horizontal waves are found in form of magnetogravitational waves (similar to waves on the f- plane) and various types of magneto-Rossby waves. In addition, the equivalence of the low-frequency mode of the magneto-Rossby wave in the Boussinesq approximation and in the magnetohydrodynamic shallow water approximation was shown. The dispersion curves of all the detected wave types are qualitatively analyzed to identify the fulfillment of the synchronism condition, which ensures the presence of three-wave interactions. A system of amplitude equations for interacting waves and the increments of two types of instability that occur in the system (decay and amplification) are obtained using the method of multiscale expansions. The difference in the coefficients and differential operators in the three-wave interaction system is shown for each of the found types of three-wave interactions.</p><p>This research was supported by the Russian Foundation for Basic Research (project no. 19-02-00016)</p>

The Darboux dressing transformation (DDT) uses known seed solutions to algebraically generate more complex, non-trivial solutions for a nonlinear system. These seeds are frequently modelled as plane waves that constitute the plane wave background upon which subsequent nonlinear structures propagate. We apply the DDT to the three-wave resonant interaction system to derive the analytical expressions for explosive solutions on a plane wave background, along with the formula for their explosion time. We also prove that these solutions exist if their plane wave background is linearly unstable in time, with a gain function that does not vanish at the zero-wavenumber of the perturbation and corresponds to a twisted loop in the stability spectrum.

We consider experimentally three-wave resonant nonlinear interactions of fields propagating in nonlinear media. We investigate the spatial dynamics of two diffractionless beams at frequency omega1, omega2 which mix to generate a field at the sum frequency omega3. If the generated field at omega3 can sustain a soliton, it decays into solitons at omega1, omega2. We report the experimental evidence of the transition from steady frequency wave generation to solitonic decay in nonlinear optics.

Jahn-Teller effect and large-amplitude motion in [formula omitted] studied by high-resolution photoelectron spectroscopy of CH4

We present anelastic and dielectric spectroscopy measurements of PbZr(1-x)Ti(x)O(3) with 0.455 < or = x < or = 0.53, which provide new information on the low-temperature phase transitions. The tetragonal-to-monoclinic transformation is first order for x < 0.48 and causes a softening of the polycrystal Young's modulus whose amplitude may exceed the one at the cubic-to-tetragonal transformation; this is explainable in terms of linear coupling between shear strain components and tilting angle of polarization in the monoclinic phase. The transition involving rotations of the octahedra below 200 K is visible both in the dielectric and anelastic losses, and it extends within the tetragonal phase, as predicted by recent first-principle calculations.

A lot has been written [1] about temporal soliton coupling using various forms of coupled Schrödinger equations and widely differing methods of solutions. They range from being almost entirely mathematical, through mixed approaches, based upon linear stability analysis, to being entirely variational [2–5]. The problems already addressed in this group have used generic coupled Schrödinger equations to yield soliton dynamics, expressed in terms of linear coupling and nonlinear coupling parameters. In this context, polarisation-coupled spatial sohtons [6] in optical planar waveguides have been investigated using Whitham’s [7] average variational principle. It is encouraging that analytical forms of the so-called stability edges have been found and the numerical work provided confirms that the true solitons agree with the mathematical analysis. In addition, the behaviour of spatial solitions in coupled planar optical waveguides has been investigated in a theory that includes all the nonlinear cross-phase modulation terms [4]. Here, problems addressed concern spatial soliton beam displacement, beam switching, and a number of stability problems. It is safe to say, then, that significant mathematical progress has been made and that, in every case, it has been verified by accurate [exact] numerical simulation.KeywordsYttrium Iron GarnetInstability ThresholdBright SolitonSpatial SolitonGarnet FilmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

There is an ever-increasing demand for longer and higher resolution numerical simulations of the weather and climate. To achieve this with reasonable wall-clock times, it is desirable to use as large a time-step as possible, whilst retaining a stable and accurate solution. However, this is very challenging in the presence of highly oscillatory linear waves; there are explicit time-step limits and losses in accuracy with implicit methods. This talk will highlight where non-linear errors can result from large time-steps and provide metrics for quantifying this. We begin by re-casting the non-linearity as a product of linear waves. In the Rotating Shallow Water Equations (RSWEs), this allows for key dynamics to be expressed as three-wave &amp;#8216;triad&amp;#8217; interactions. A non-linear &amp;#8216;triadic&amp;#8217; time-stepping error is computed using linear stability polynomials. A number of explicit and implicit time-stepping methods (such as RK4, TR-BDF2, ETD-RK2) will be compared analytically in the RSWEs. Next, two new test problems enable analyses of large time-step simulations. The first is of a Gaussian perturbation to a RSWE height field. A proposed metric, relating to the kinetic energy distribution over temporal frequency, quantifies phase errors in the height reformation. The second test case initialises linear waves which, via direct- and near- resonant triad interactions, will construct non-linear dynamics. Phase errors with large time-steps can be identified in the corresponding height fields. A first variant of this case will initialise only two waves; this will primarily instigate an energy exchange within a dominant triad. A second version, containing more slow modes, enables a re-distribution of fast mode energy into rings in wavenumber space.

Triplet exciton absorption lines in pure anthracene and pyrene crystals are investigated at very high resolution using photoexcitation in the lower temperature (<90 K) regime. The profiles for the lower Davydov components (zero-phonon) are observed to be most sensitive to crystal quality. Linewidths as small as 0.02 cm−1 are observed for the lowest exciton of anthracene with the upper component about 50 times broader. The T-dependences of the linewidths for the Davydov components of anthracene are shown to be explicable in terms of combined linear and quadratic exciton-photon coupling. The T-dependence of the zero-phonon to phonon sideband intensity ratio for pyrene is well described by the linear exciton-photon interaction in which the exciton is taken to be localized.

The magnetostatic waves (MSW) are dispersive in ferromagnetic film wave guide and exhibit wave vector anisotropy so that, in general, the energy flow and wave vector are noncollinear. This paper investigates the dependence of the energy flow direction of linear magnetostatic surface waves (MSSW), volume waves (MSVW), and nonlinear MSSW on the direction of the bias magnetic field H.

We study high-energy elastic and inelastic processes in a ${\ensuremath{\phi}}^{3}$ theory based on the following model: For the elastic-scattering amplitude we first sum the leading terms in each order of perturbation of the $t$-channel straight ladders, plus those obtained by interchange of the Mandelstam variables $s$ and $u$. We then perform the $s$-channel iteration with the $t$-channel ladders as single units. We are only interested in the physical regions in which the incident particles retain their large momenta. This procedure leads to the eikonalization of the $t$-channel ladders. For the inelastic production amplitude, the dominant contribution comes from diagrams with any number of totally open ladders (i.e., multiperipheral chains) modified by unopen ones. The main results are: (a) The total cross section approaches zero, approaches a constant, or increases as ${(\mathrm{lns})}^{2}$ according as the coupling constant is smaller than, equal to, or larger than a critical value. (b) Elastic and inelastic differential cross sections are computed, and they have many nice features, as suggested by the absorption model. (c) Nonforward $s$-channel unitarity is explicitly verified. (d) One-particle and multiparticle spectra, the average multiplicity, the number distribution of the final particles, etc., are obtained. The implications of these results to hadron physics are discussed.

Marine planktonic ciliates are a link between microbial food web and classical food chain. They play a pivotal role in material cycling and energy flow in marine ecosystem. Since the 1970s,growth rates of marine planktonic ciliates have been studied in both laboratory and in situ. Only few laboratory studies on ciliate growth rates are available in China, and no field research has been carried out to determine the growth rates of planktonic ciliates. This review summarizes previous studies on the growth rates in both laboratory and in situ. Laboratory experiments show that the growth rates varied with food type and temperature. Under a certain temperature,ciliate would stop growing or die when food availability is below its threshold value. The growth rates could increase as food concentration increase over the threshold value,and then reach intrinsic growth rate( μmax),stay or drop slightly at a high food concentrations. Scientists estimated the μmaxvalues of 34 oligotrichous ciliate species in laboratory; and the values ranged 0. 1—3. 05 d-1. Feeding on a given prey,ciliate would stop growing or die at low temperature. μmaxincreased linearly with temperature in the intermediate range. Higher pH will restrain μmax. Size-fractionated seawater incubation was used to estimate in situ ciliate growth rate,from which the maximum growth rate was 3. 3 d-1. Temperature,hypoxia,and prey( bottom up control) influenced the ciliate growth rate in differentregions. Planktonic ciliate production,calculated according to ciliate abundance and growth rate,was higher than planktonic copepod production in most cases.

In this paper, a three-wave resonant interaction system, which describes the mixture of waves with different frequencies in a weakly nonlinear and dispersive medium, is investigated with the help of the Darboux transformation and its extension. Firstly, we construct the dark–bright–bright mixed multi-soliton solutions in terms of the determinant. Dark–bright–bright solitons are found to arise in the focusing, defocusing and mixed cases. Bound state of the two dark–bright–bright solitons is also analyzed. Secondly, we derive the dark–bright–bright mixed high-order semi-rational solitons and find that their structures are different from the multi-soliton ones. Finally, we present the Nth-order breather solutions in terms of the determinant, where N is a positive integer. Line-shaped and three wing-shaped structures of the breathers are obtained.