Related papers: Stability and dynamics of two-soliton molecules
In the recent work "Non-reciprocal topological solitons in active metamaterials" (see arXiv:2312.03544v1), for an analytical understanding of the system under consideration, the authors derive an ordinary differential equation for the…
We study two-dimensional stationary soliton gas in the framework of the time-independent reduction of the Kadomtsev-Petviashvili (KPII) equation, which coincides with the integrable two-way ``good'' Boussinesq equation in the xy-plane. This…
We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schr\"odinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical…
In recent times, bound soliton states have often been referred to as soliton molecules in the nonlinear optics literature. The striking analogies between photonic bound states and matter molecular structures in chemistry and physics have…
We introduce discrete multivortex solitons in a ring of nonlinear oscillators coupled to a central site. Regular clusters of discrete vortices appear as a result of mode collisions and we show that their stability is determined by global…
The evolution of vector solitons under nonlinearity management is studied. The averaged over strong and rapid modulations in time of the inter-species interactions vector Gross-Pitaevskii equation (GPE) is derived. The averaging gives the…
We present a detailed numerical study of the stability under periodic perturbations of line solitons of two-dimensional, generalized Zakharov-Kuznetsov equations with various power nonlinearities. In the $L^{2}$-subcritical case, in…
We consider dynamical stabilization of Bose-Einstein condensates (BEC) by time-dependent modulation of the scattering length. The problem has been studied before by several methods: Gaussian variational approximation, the method of moments,…
Soliton molecules are the manifestation of attractive and repulsive interaction between optical pulses mediated by a nonlinear medium. However, the formation and breakup of soliton molecules are difficult to observe due to the transient…
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field…
The dynamics of a two-soliton molecule bouncing on the reflecting atomic mirror under the effect of gravity has been studied by analytical and numerical methods. The analytical description is based on the variational approximation. In…
The dynamics of a two-component dilute Bose gas of atoms at zero temperature is described in the mean field approximation by a two-component Gross-Pitaevskii Equation. We solve this equation assuming a Gaussian shape for the wavefunction,…
The theory of linear dispersive equations predicts that waves should spread out and disperse over time. However, it is a remarkable phenomenon, observed both in theory and practice, that once nonlinear effects are taken into account,…
Solitons are self-sustained wavepackets that occur in many physical systems. Their recent demonstration in optical microresonators has provided a new platform for study of nonlinear optical physics with practical implications for…
We study coherent dynamics of two interacting Bose-Bose droplets by means of the extended Gross-Pitaevskii equation. The relative motion of the droplets couples to the phases of their components. The dynamics can be understood in terms of…
In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in…
This paper studies the behavior of solitons in the Korteweg-de Vries equation under the influence of multiplicative noise. We introduce stochastic processes that track the amplitude and position of solitons based on a rescaled frame…
The dynamics of two-component solitons with a small spatial displacement of the high-frequency (HF) component relative to the low-frequency (LF) one is investigated in the framework of the Zakharov-type system. In this system, the evolution…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
The stability of an expanding parton plasma is analyzed within quasi-particle models. The effective mass of the parton is calculated self-consistently from a gap equation which is either obtained from the Nambu Jona-Lasinio Lagrangian or…