arXiv subjects

Sergey Nazarenko

Publications and source records attributed to Sergey Nazarenko.

At least 19 recordsLinked to original sources

arXiv2026

Dissipation-driven champion solitons in one-dimensional shallow-water waves

In this paper, we identify a new mechanism for rogue wave formation in a shallow-water setting. We study a bidirectional shallow-water wave field in the context of the Kaup-Boussinesq equation, and introduce a weak high-wavenumber dissipative perturbation that breaks the underlying integrability of the system. In this setting, dominant solitons grow through successive interactions with weaker, co-propagating solitons, leading to the formation of a "champion soliton" in each direction of propagation. This behaviour is in contrast to the general intuition that dissipation damps coherent structures, and instead shows that weak dissipation can induce their intensification. Moreover, we find that weak dissipation alone is not sufficient for champion soliton formation; the presence of random waves plays a crucial role in the intensification process, catalysing the transfer of energy into dominant coherent structures. While champion solitons have previously been studied in non-integrable systems, these works primarily consider perturbations introduced through modifications of the nonlinear terms (e.g., higher-order Korteweg-de Vries and Schrödinger-type models). In the present work, high-wavenumber dissipation provides a more physically natural perturbation, since such small-scale damping is a common feature in many systems.

nlin.PS↗

arXiv2026

Universal self-similar evolution of two-dimensional acoustic turbulence in Bose-Einstein condensates

When driven out of equilibrium, a Bose-Einstein condensate develops nonlinearly interacting density waves that trigger a turbulent cascade, transferring energy toward small scales. In this Letter, we investigate the nonstationary evolution of solutions to the two-dimensional Gross-Pitaevskii equation (GPE). Through numerical simulations of both the GPE and the corresponding Wave Kinetic Equation (WKE), we identify self-similar solutions relevant to turbulence in atomic and polariton Bose-Einstein Condensates. These solutions correspond to a new type of non-thermal fixed point and exhibit characteristics of both first and second kind self-similarity. In particular, we show that the dynamics of the propagating front is universal, governed by a dimensionless universal constant $β$, which we determine numerically.

cond-mat.quant-gas↗

arXiv2026

Wave Kinetics and Thermalization in Kadomtsev-Petviashvili-I System

We study properties of solutions, both evolving and equilibrium of the wave-kinetic equation describing ensembles of weak random waves governed by the Kadomstev-Petviashivli-I equations. The latter equation is integrable by the inverse scattering method, and yet it allows resonant wave interactions leading to redistribution of energy in the Fourier space. Such resonant interactions preserve an infinite number of invariants and we find that they preserve compactness of Fourier space supports. Numerically, we observe that the system can thermalize to one of the equilibrium states of Rayleigh-Jeans type, despite the common empirical belief that thermalization is impossible for integrable systems. The thermalized states are formed via non-local spectral transfers leading to creation of strong low-wavenumber peaks of the wave spectrum -- a process akin to Bose-Einstein condensation.

nlin.CD↗

arXiv2026

Dynamical cooling driven by self-similar fronts in the 2D nonlinear Schrödinger model

We analyze the dynamics towards partial thermalization and subsequent cooling in the defocusing two-dimensional nonlinear Schrödinger model, using direct simulations and insights from the wave-kinetic equations (WKE) and a fourth-order differential approximation model (DAM). We show that the evolving WKE spectrum exhibits two distinct similarity ranges--the quasi-thermal core and the ultraviolet tail--whereas in the DAM, an additional range of infrared self-similarity appears. By stretching the quasi-thermal region, the self-similar fronts drive an effective dynamical cooling process towards the formal but ill-defined equilibrium state at vanishing temperature--analogous to an ultraviolet catastrophe in a system of classical waves.

math-ph↗

arXiv2026

Turbulence and far-from-equilibrium equation of state of Bogoliubov waves in Bose-Einstein Condensates

Bogoliubov waves are fundamental excitations of Bose-Einstein Condensates (BECs). They emerge from a perturbed ground state and interact nonlinearly, triggering turbulent cascades. Here, we study turbulent BECs theoretically and numerically using the 3D Gross-Pitaevskii model and its associated wave-kinetic equations. We derive a new Kolmogorov-like stationary spectrum for short Bogoliubov waves and find a complete analytical expression for the spectrum in the long-wave acoustic regime. We then use our predictions to explain the BEC equation of state reported by Dogra et al. (Nature 620, 521, 2023), and to suggest new experimental settings.

cond-mat.quant-gas↗

arXiv2026

Strong and weak wave turbulence regimes in Bose-Einstein condensates

When a turbulent Bose-Einstein condensate is driven out-of-equilibrium at a scale much smaller than the system size, nonlinear wave interactions transfer particles towards large scales in an inverse cascade process. In this work, we study numerically wave turbulence in a three-dimensional Bose-Einstein condensate in forced and dissipated inverse cascade settings. We observe that when the forcing rate increases, thereby increasing the particle flux, the turbulence spectrum gradually transitions from the weak-wave Kolmogorov-Zakharov cascade to a critical balance state characterized by a range of scales with balanced linear and nonlinear dynamic timescales. Further forcing increases lead to a coherent condensate component superimposed with Bogoliubov-type acoustic turbulence. The role of vortices in such a strongly forced state is marginal, which makes this new state very different from the strongly turbulent state composed of a tangle of quantized vortex lines. We then use our predictions and numerical data to formulate a new out-of-equilibrium equation of state for the 3D inverse cascade.

cond-mat.quant-gas↗

arXiv2026

Bidirectional shallow-water wave turbulence

We study bidirectional one-dimensional (1-D) shallow-water waves within a class of Boussinesq equations, including the integrable Kaup-Boussinesq (KB) equation and a truncated-dispersion variant, which serves as a representative non-integrable model. For these two systems, the normal-form transformation yields an interaction coefficient of the same general structure, differing only through the dispersion relation. We derive this coefficient and numerically confirm that it vanishes on the resonant manifold for the KB equation, as expected in the literature. In contrast, the non-integrable model admits a non-vanishing interaction coefficient, producing a non-trivial wave kinetic equation (WKE), which is the first known in a 1-D shallow-water setting. The resulting WKE is non-homogeneous in nature due to the non-homogeneity of the corresponding dispersion relation; however, approximate Kolomogrov-Zakharov (KZ) solutions can be derived in a novel way under certain approximations. Numerical experiments in two settings validate the kinetic predictions and elucidate the underlying dynamics: (i) in free-evolution cases of the KB equation, despite complete integrability and the invariance of the discrete nonlinear spectrum guaranteed by isospectrality, an initial arbitrary wavenumber spectrum undergoes substantial evolution driven by quasi-resonant triad interactions; (ii) in forced-dissipated cases of the non-integrable equation, we find stationary power-law spectra that agree with the theoretical predictions.

nlin.CD↗

arXiv2026

Universal Behavior on the Relaxation Dynamics of Far-From-Equilibrium Quantum Fluids

Investigating the initial conditions that lead many-body quantum systems to an out-of-equilibrium state is fundamental for understanding their thermalization dynamics. In this work we observe the relaxation for two regimes of excitation that can drive the turbulent Bose-Einstein condensate into two distinct final states, and are defined by the amount of energy injected into the system. The subcritical regime is characterized by a lower injection of energy, which can lead to an inverse particle cascade and, consequently, to the BEC mode repopulation during the relaxation process. The supercritical regime is marked by a higher energy injection, that may lead to the BEC dissolution and a final thermal state. In both cases we observe relaxation stages that exhibit the same key features: a direct cascade, a non-thermal fixed point with the same exponents, a prethermalization region and, finally, the thermalization of the system. In the final thermalization stage, universal scaling is observed for both regimes, even though their final states are completely different. By analyzing the coherence length of our turbulent cloud, we clearly visualize the recovery and the loss of the coherence for the subcritical and supercritical regimes after relaxation. These results indicate that the evolution of turbulence occurs independent of its initial conditions and of the final state achieved.

cond-mat.quant-gas↗

arXiv2026

Stability of stationary solutions in Acoustic wave turbulence

We study the stability of steady-state solutions of the Wave-Kinetic Equations for acoustic waves. Combining theoretical analysis and numerical simulations, we characterise the time evolution of small isotropic perturbations for both 2D and 3D equilibrium Rayleigh-Jeans and non-equilibrium Kolmogorov-Zakharov solutions. In particular, we show that the stability of these solutions is ensured by different mechanisms.

nlin.CD↗

arXiv2025

A bound state attractor in optical turbulence

We study numerically the nonintegrable dynamics of coherent, solitonic, nonlinear waves, in a spatially nonlocal nonlinear Schrodinger equation relevant to realistic modelling of optical systems: the Schrodinger-Helmholtz equation. We observe a single oscillating, coherent solitary wave emerging from a variety of initial conditions. Using the direct scattering transform of the (integrable) cubic nonlinear Schrodinger equation, we find that this structure is a bound state, comprising of a primary and secondary soliton whose amplitudes oscillate out of phase. We interpret this as the solitons periodically exchanging mass. We observe this bound state self-organising from a state of incoherent turbulence, and from solitonic structures launched into the system. When a single (primary) solitonic structure is launched, a resonance process between it and waves in the system generates the secondary soliton, resulting in the bound state. Further, when two solitons are initially launched, we show that they can merge if their phases are synchronised when they collide. When the system is launched from a turbulent state comprised of many initial solitons, we propose that the bound state formation is preceded a sequence of binary collisions, in which the mass is transferred on average from the weak soliton to the strong one, with occasional soliton mergers. Both processes lead to increasingly stronger and fewer dominant solitons. The final state -- a solitary double-solitonic bound state surrounded by weakly nonlinear waves -- is robust and ubiquitous. We propose that for nonlocal media, it is a more typical statistical attractor than a single-soliton attractor suggested in previous literature.

nlin.PS↗

arXiv2025

Wave-kinetic dynamics of forced-dissipated turbulent internal gravity waves

Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. To investigate their dynamics, we perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy spectrum of weakly nonlinear internal gravity waves. During the early evolution, three well-known nonlocal interactions, the Elastic Scattering, the Induced-Diffusion, and the Parametric Subharmonic Instability, together with a Superharmonic Resonance play a prominent role. In contrast, local interactions are responsible for anisotropic energy cascade on longer time scales. We reveal emergence of a condensate at small horizontal wavevectors that can be interpreted as a pure wave-wave interaction-mediated layering process.

physics.flu-dyn↗

arXiv2024

Semi-local one-dimensional optical wave turbulence

We study one-dimensional optical wave turbulence described by the 1D Schr{ö}dinger-Helmholtz model for nonlinear light propagation in spatially nonlocal nonlinear optical media such as nematic liquid crystals. By exploiting the specific structure of the nonlocal response, we derive a reduced wave kinetic equation under a semi-local approximation that permits the study of weak-wave turbulent cascades. We explore the realisability of the wave turbulence predictions and demonstrate new turbulent behaviour related to spatial nonlocality. Moreover, we show strong dependence of the wave turbulence to the possible presence of incoherent solitonic structures.

physics.optics↗

arXiv2024

On the kinetics of internal gravity waves beyond the hydrostatic regime

We present a new derivation of the kinetic equation for weak, non-hydrostatic internal gravity wave turbulence. The equation is equivalent to the one obtained by Caillol & Zeitlin (2000), but it takes a canonical form. We show that it conserves the energy without involving the resonance condition in frequency, and look for the isotropic part of the steady, scale invariant solutions. We provide a parametrization of the resonant manifold of non-hydrostatic internal gravity wave triadic interactions. This allows us to simplify the collision integral, and to evaluate the transfer coefficients of all triadic interactions. In the hydrostatic limit, our equation is equivalent to the Hamiltonian description of Lvov & Tabak (2001).

physics.flu-dyn↗

arXiv2023

Self-similar evolution of wave turbulence in Gross-Pitaevskii system

We study the universal non-stationary evolution of wave turbulence (WT) in Bose-Einstein condensates (BECs). Their temporal evolution can exhibit different kinds of self-similar behavior corresponding to a large-time asymptotic of the system or to a finite-time blowup. We identify self-similar regimes in BECs by numerically simulating the forced and unforced Gross-Pitaevskii equation (GPE) and the associated wave kinetic equation (WKE) for the direct and inverse cascades, respectively. In both the GPE and the WKE simulations for the direct cascade, we observe the first-kind self-similarity that is fully determined by energy conservation. For the inverse cascade evolution, we verify the existence of a self-similar evolution of the second kind describing self-accelerating dynamics of the spectrum leading to blowup at the zero mode (condensate) at a finite time. We believe that the universal self-similar spectra found in the present paper are as important and relevant for understanding the BEC turbulence in past and future experiments as the commonly studied stationary Kolmogorov-Zakharov (KZ) spectra.

cond-mat.other↗

arXiv2023

Internal gravity waves in stratified flows with and without vortical modes

The comprehension of stratified flows is important for geophysical and astrophysical applications. The Weak Wave Turbulence theory aims to provide a statistical description of internal gravity waves propagating in the bulk of such flows. However, internal gravity waves are usually perturbed by other structures present in stratified flow, namely the shear modes and the vortical modes. In order to check whether a weak internal gravity wave turbulence regime can occur, we perform direct numerical simulations of stratified turbulence without shear modes, and with or without vortical modes at various Froude and buoyancy Reynolds numbers. We observe that removing vortical modes naturally helps to have a better overall balance between poloidal kinetic energy, involved in internal gravity waves, and potential energy. However, conversion between kinetic energy and potential energy does not necessarily show fluctuations around zero in our simulations, as we would expect for a system of weak waves. A spatiotemporal analysis reveals that removing vortical modes helps to concentrate the energy around the wave frequency, but it is not enough to observe a weak wave turbulence regime. Yet, we observe that internal gravity waves whose frequency are large compared to the eddy turnover time are present, and we also find evidences for slow internal gravity waves interacting by Triadic Resonance Instabilities in our strongly stratified flows simulations. Finally, we propose conditions that should be fulfilled in order to observe a weak internal gravity waves turbulence regime in real flows.

physics.flu-dyn↗

arXiv2023

Initial evolution of 3D turbulence en route to the Kolmogorov state: emergence and transformations of coherent structures, self-similarity and instabilities

In this work, we study numerically the temporal evolution of an initially random large-scale velocity field under governed by the hyperviscous incompressible Navier-Stoke equations. Three stages are clearly observed during the evolution. First, the initial condition development is characterized by a spectrum evolving in a self-similar way with a wave number front $k_*(t)$ propagating toward high values exponentially in time. This evolution corresponds to the formation and shrinking of think vortex pancakes exponentially in time, as it has been previously reported in simulations of the incompressible Euler equations. At the second stage, pancakes become unstable, rolling up on the edges and breaking up in the middle, leading to the emergence of vortex ribs -- quasi-periodic arrangements of vortex filaments. Those filaments then twist creating structures akin to ropes. At the last stage, a fully developed turbulent state is observed, characterized by a Kolmogorov energy spectrum and exhibiting a decay law compatible with standard turbulent predictions in the case of an integral scale saturated at the scale of the box.

physics.flu-dyn↗

arXiv2023

An effective semilocal model for wave turbulence in 2D nonlinear optics

The statistical evolution of ensembles of random, weakly-interacting waves is governed by wave kinetic equations. To simplify the analysis, one frequently works with reduced differential models of the wave kinetics. However, the conditions for deriving such reduced models are seldom justified self-consistently. Here, we derive a reduced model for the wave kinetics of the Schr{ö}dinger-Helmholtz equations in two spatial dimensions, which constitute a model for the dynamics of light in a spatially-nonlocal, nonlinear optical medium. This model has the property of sharply localising the frequencies of the interacting waves into two pairs, allowing for a rigorous and self-consistent derivation of what we term the semilocal approximation model (SLAM) of the wave kinetic equation. Using the SLAM, we study the stationary spectra of Schr{ö}dinger-Helmholtz wave turbulence, and characterise the spectra that carry energy downscale, and waveaction upscale, in a forced-dissipated setup. The latter involves a nonlocal transfer of waveaction, in which waves at the forcing scale mediate the interactions of waves at every larger scale. This is in contrast to the energy cascade, which involves local scale-by-scale interactions, familiar from other wave turbulent systems and from classical hydrodynamical turbulence.

physics.optics↗

arXiv2023

Direct and inverse cascades in turbulent Bose-Einstein condensate

When a Bose-Einstein condensate (BEC) is driven out of equilibrium, density waves interact non-linearly and trigger turbulent cascades. In a turbulent BEC, energy is transferred towards small scales by a direct cascade, whereas the number of particles displays an inverse cascade toward large scales. In this work, we study analytically and numerically the direct and inverse cascades in wave-turbulent BECs. We analytically derive the Kolmogorov-Zakharov spectra, including the log-correction to the direct cascade scaling and the universal pre-factor constants for both cascades. We test and corroborate our predictions using high-resolution numerical simulations of the forced-dissipated Gross-Pitaevskii model in a periodic box and the corresponding wave-kinetic equation. Theoretical predictions and data are in excellent agreement, without adjustable parameters. Moreover, in order to connect with experiments, we test and validate our theoretical predictions using the Gross-Pitaevskii model with a confining cubic trap. Our results explain previous experimental observations and suggest new settings for future studies.

cond-mat.quant-gas↗