arXiv subjects

Dimitrios J. Frantzeskakis

Publications and source records attributed to Dimitrios J. Frantzeskakis.

17 recordsLinked to original sources

arXiv2026

Perturbation theory for kinks of the defocusing modified Korteweg-de Vries equation

In this work we develop an integrable perturbation theory for the defocusing modified Korteweg-de Vries kink solution based on the squared eigenfunction expansion associated with the underlying Zakharov-Shabat scattering problem. We derive the completeness relation for the squared eigenfunctions appropriate to the kink background, establish the adjoint structure needed to handle perturbations of both the continuous and discrete spectral components, and obtain explicit evolution equations for the perturbed kink parameters at leading order. The study of the first order correction shows that perturbations generically produce a radiative shelf in front of the kink. We also apply our results to certain physically relevant perturbations and show that the predictions are consistent with direct numerical simulations.

nlin.SI↗

arXiv2026

Rogue waves in extended Gross-Pitaevskii Models with a Lee-Huang-Yang correction

We explore the existence and dynamical generation of rogue waves (RWs) within a one dimensional quantum droplet bearing environment. RWs are computed by deploying a spacetime fixed point scheme to the relevant extended Gross Pitaevskii equation (eGPE). Parametric regions where the ensuing RWs are different from their counterparts in the nonlinear Schroedinger equation are identified. To corroborate the controllable generation, relevant to ultracold atom experiments, of these rogue patterns we exploit two different protocols. The first is based on interfering dam break flows emanating from Riemann initial conditions and the second refers to the gradient catastrophe of a spatially localized waveform. A multitude of possible RWs are found in this system, spanning waveforms reminiscent of the Peregrine soliton, its spatially periodic variants, namely, the Akhmediev breathers, and other higher order RW solutions of the nonlinear Schroedinger equation. Key elements of the shape of the corresponding eGPE RWs traced back to nonintegrability and the presence of competing interactions are discussed. Our results set the stage for probing a multitude of unexplored rogue like waveforms in such mixtures with competing interactions and should be accessible to current ultracold atom experiments.

cond-mat.quant-gas↗

arXiv2025

Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices

The time evolution of initially localized wavepackets in the discrete Hatano-Nelson lattice displays a rich dynamical structure shaped by the interplay between dispersion and nonreciprocity. Our analysis reveals a characteristic evolution of the wave-packet center of mass, which undergoes an initial acceleration, subsequently slows down, and ultimately enters a regime of uniform motion, accompanied throughout by exponential amplification of the wave-packet amplitude. To capture this behavior, we develop a continuum approximation that incorporates higher-order dispersive and nonreciprocal effects and provides accurate analytical predictions across all relevant time scales. Building on this framework, we then demonstrate the existence of a non-Hermiticity-induced jump - an abrupt spatial shift of the wave-packet center even in the absence of disorder - and derive its underlying analytical foundation. The analytical predictions are in excellent agreement with direct numerical simulations of the Hatano-Nelson chain. Our results elucidate the interplay between dispersion and nonreciprocity in generating unconventional transport phenomena, and pave the way for controlling wave dynamics in nonreciprocal and non-Hermitian metamaterials.

cond-mat.mes-hall↗

arXiv2025

NLS approximation and dark solitons for the Adlam-Allen model of cold collisionless plasmas

The present work extends earlier considerations on a quintessential model of cold, collisionless plasmas, namely the Adlam-Allen model. Previously, an analysis of homoclinic solutions around a non-vanishing background (associated with a saddle equilibrium) led to a Korteweg-de Vries reduction. Here, we consider a different equilibrium of the co-traveling frame model, namely a center, and expanding around it, by means of a multiple-scale methodology and suitable scalings, leads to an effective defocusing nonlinear Schr{ö}dinger equation. Leveraging the latter, we construct, for the first time to our knowledge, physically realistic dark soliton waveforms of the Adlam-Allen model. We subsequently test the numerical evolution of such coherent structures, identifying them as long-lived waveforms of the full model.

nlin.PS↗

arXiv2025

On shallow water non-convex dispersive hydrodynamics: the extended KdV model

In this work, we investigate non-classical wavetrain formations, and particularly dispersive shock waves (DSWs), or undular bores, in systems exhibiting non-convex dispersion. Our prototypical model, which arises in shallow water wave theory, is the extended Korteweg-de Vries (eKdV) equation. The higher-order dispersive and nonlinear terms of the latter, lead to resonance between dispersive radiation and solitary waves, and notably, the individual waves comprising DSWs, due to non-convex dispersion. This resonance manifests as a resonant wavetrain propagating ahead of the dispersive shock wave. We present a succinct overview of the fundamental principles and characteristics of DSWs and explore analytical methods for their analysis. Wherever applicable, we demonstrate these concepts and techniques using both the classical KdV equation and its higher-order eKdV counterpart. We extend the application of the dispersive shock fitting method and the equal amplitude approximation to investigate radiating DSWs governed by the eKdV equation. We also introduce Whitham shock solutions for the regime of traveling DSWs of the eKdV model. Theoretical predictions are subsequently validated against direct numerical solutions, revealing a high degree of agreement.

nlin.PS↗

arXiv2025

Harnessing Nonlinearity to Tame Wave Dynamics in Nonreciprocal Active Systems

We present a mechanism to generate unidirectional pulse-shaped propagating waves, tamed to exponential growth and dispersion, in active systems with nonreciprocal and nonlinear couplings. In particular, when all bulk modes are exponentially localized at one side of the lattice (skin effect), it is expected that wave dynamics is governed by amplification or decay until reaching the boundaries, even in the presence of dissipation. Our analytical results, and experimental demonstrations in an active electrical transmission line metamaterial, reveal that nonlinearity is a crucial tuning parameter in mediating a delicate interplay between nonreciprocity, dispersion, and dissipation. Consequently, undistorted unidirectional solitonic pulses are supported both for low and high nonreciprocity and pulse amplitude strength. The proposed mechanism facilitates robust pulse propagation in signal processing and energy transmission applications.

cond-mat.mes-hall↗

arXiv2022

Interactions of solitary waves in the Adlam-Allen model

We study the interactions of two or more solitary waves in the Adlam-Allen model describing the evolution of a (cold) plasma of positive and negative charges, in the presence of electric and transverse magnetic fields. In order to show that the interactions feature an exponentially repulsive nature, we elaborate two distinct approaches: (a) using energetic considerations and the Hamiltonian structure of the model; (b) using the so-called Manton's method. We compare these findings with results of direct simulations, and identify adjustments necessary to achieve a quantitative match between them. Additional connections are made, such as with solitons of the Korteweg--de Vries equation. New challenges are identified in connection to this model and its solitary waves.

nlin.PS↗

arXiv2022

Acoustic solitons in a periodic waveguide: theory and experiments

We study the propagation of high-amplitude sound waves, in the form of pulse-like solitary waves, in an air-filled acoustic waveguide of periodically varying cross section. Our numerical simulations, solving the compressible Navier-Stokes equations in two dimensions, as well as our experimental results, strongly suggest that nonlinear losses, originated from vortex shedding (at the segment changes) are crucial in the dynamics of high amplitude pulses. We find that, even in the presence of strong dissipation, the solitary wave roughly retains its characteristics (as described by the amplitude-velocity-width relations), obtained by the derivation and analysis of an effective Boussinesq equation. In addition, we propose a transmission-line based numerical scheme, able to capture well the experimental results. The proposed design offers a new playground for the study of the combined effects of dispersion, nonlinearity and dissipation in air-borne acoustics, while, due to its simplicity, it can be extended to higher dimensions.

nlin.PS↗

arXiv2022

Extended shallow water wave equations

Extended shallow water wave equations are derived, using the method of asymptotic expansions, from the Euler (or water wave) equations. These extended models are valid one order beyond the usual weakly nonlinear, long wave approximation, incorporating all appropriate dispersive and nonlinear terms. Specifically, first we derive the extended Korteweg-de Vries (KdV) equation, and then proceed with the extended Benjamin-Bona-Mahony and the extended Camassa-Holm equations in (1+1)-dimensions, the extended cylindrical KdV equation in the quasi-one dimensional setting, as well as the extended Kadomtsev-Petviashvili and its cylindrical counterpart in (2+1)-dimensions. We conclude with the case of the extended Green-Naghdi equations.

physics.flu-dyn↗

arXiv2021

Nematic dispersive shock waves from nonlocal to local

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonant is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations and excellent agreement is found.

nlin.PS↗

arXiv2020

Solitary and Periodic Waves in Collisionless Plasmas: The Adlam-Allen Model Revisited

We consider the Adlam-Allen (AA) system of partial differential equations which, arguably, is the first model that was introduced to describe solitary waves in the context of propagation of hydrodynamic disturbances in collisionless plasmas. Here, we identify the solitary waves of the model by implementing a dynamical systems approach. The latter suggests that the model also possesses periodic wave solutions --which reduce to the solitary wave in the limiting case of infinite period-- as well as rational solutions which are obtained herein. In addition, employing a long-wave approximation via a relevant multiscale expansion method, we establish the asymptotic reduction of the AA system to the Korteweg-de Vries equation. Such a reduction, is not only another justification for the above solitary wave dynamics, but also may offer additional insights for the emergence of other possible plasma waves. Direct numerical simulations are performed for the study of multiple solitary waves and their pairwise interactions. The stability of solitary waves is discussed in terms of potentially relevant criteria, while the robustness of spatially periodic wave solutions is touched upon by our numerical experiments.

nlin.PS↗

arXiv2018

Continuous families of solitary waves in non-symmetric complex potentials: A Melnikov theory approach

The existence of stationary solitary waves in symmetric and non-symmetric complex potentials is studied by means of Melnikov's perturbation method. The latter provides analytical conditions for the existence of such waves that bifurcate from the homogeneous nonlinear modes of the system and are located at specific positions with respect to the underlying potential. It is shown that the necessary conditions for the existence of continuous families of stationary solitary waves, as they arise from Melnikov theory, provide general constraints for the real and imaginary part of the potential, that are not restricted to symmetry conditions or specific types of potentials. Direct simulations are used to compare numerical results with the analytical predictions, as well as to investigate the propagation dynamics of the solitary waves.

nlin.PS↗

arXiv2017

Light meets water in nonlocal media: Surface tension analogue in optics

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in $(2+1)$-dimensions. We identify an analogue of surface tension in optics, namely a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvilli (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality.

nlin.PS↗

arXiv2017

Bright and Gap Solitons in Membrane-Type Acoustic Metamaterials

We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement.

nlin.PS↗

arXiv2016

Vector nematicons

Families of soliton pairs, namely vector solitons, are found within the context of a coupled nonlocal nonlinear Schrodinger system of equations, as appropriate for modeling beam propagation in nematic liquid crystals. In the focusing case, bright soliton pairs have been found to exist provided their amplitudes satisfy a specific condition. In our analytical approach, focused on the defocusing regime, we rely on a multiscale expansion methods, which reveals the existence of dark-dark and antidark-antidark solitons, obeying an effective Korteweg-de Vries equation, as well as dark-bright solitons, obeying an effective Mel'nikov system. These pairs are discriminated by the sign of a constant that links all physical parameters of the system to the amplitude of the stable continuous wave solutions, and, much like the focusing case, the solitons' amplitudes are linked leading to mutual guiding.

nlin.PS↗

arXiv2016

Asymptotic reductions and solitons of nonlocal nonlinear Schrödinger equations

Asymptotic reductions of a defocusing nonlocal nonlinear Schrödinger model in $(3+1)$-dimensions, in both Cartesian and cylindrical geometry, are presented. First, at an intermediate stage, a Boussinesq equation is derived, and then its far-field, in the form of a variety of Kadomtsev-Petviashvilli (KP) equations for right- and left-going waves, is found. KP models include versions of the KP-I and KP-II equations, in Cartesian and cylindrical geometry. Solitary waves solutions, planar or ring-shaped, and of dark or anti-dark type, are also predicted to occur. Their nature and stability is determined by a parameter defined by the physical parameters of the original nonlocal system. It is thus found that (dark) anti-dark solitary waves are only supported by a weak (strong) nonlocality, and are unstable (stable) in higher-dimensions. Our analytical predictions are corroborated by direct numerical simulations.

nlin.PS↗

arXiv2016

Ring dark and anti-dark solitons in nonlocal media

Ring dark and anti-dark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable continuous-wave background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvilli (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties.

physics.optics↗