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Recent experimental advances in realizing degenerate quantum dipolar gases in optical lattices and the flexibility of experimental setups in attaining various geometries offer the opportunity to explore exotic quantum many-body phases…
In many crystals with sufficient anharmonicity, a special kind of lattice vibrations, namely, discrete breathers (DBs) can be excited either thermally or by external triggering, in which the amplitude of atomic oscillations greatly exceeds…
Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the uni-directional nonlinear Schr\"odinger equation…
The Dicke model describes the coherent interaction of a laser-driven ensemble of two level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature…
The Discrete Nonlinear Schr\"odinger (DNLS) equation is a Hamiltonian model displaying an extremely slow relaxation process when discrete breathers appear in the system. In [Iubini S, Chirondojan L, Oppo G L, Politi A and Politi P 2019…
We review recent studies about quantum discrete breathers. We describe their basic properties in comparison with their classical counterparts, and the ways they may be addressed theoretically in different quantum lattice models including…
We study diffusion of the Josephson phase in the asymmetric SQUID subjected to a time-periodic current and pierced by an external magnetic flux. We analyze a relation between phase diffusion and quality of transport characterized by the dc…
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions:…
We study the excitations of dark solitons in a nonlinear optical fiber with the second- and fourth-order dispersion, and find the emergence of striped dark solitons (SDSs) and some multi-dark-soliton bound states. The SDSs can exhibit…
We developed an exact theory of the super-regular (SR) breathers of Manakov equations. We have shown that the vector SR breathers do exist both in the cases of focusing and defocusing Manakov systems. The theory is based on the eigenvalue…
By means of a modified Lugiato-Lefever equation model, we investigate the nonlinear dynamics of dissipative wave structures in coherently-driven Kerr cavities with a parabolic potential. The potential stabilizes system dynamics, leading to…
A transmission line coupled to an externally driven superconducting quantum interference device (SQUID) can exhibit the Dynamical Casimir Effect (DCE). Employing this setup, we quantize the SQUID degrees of freedom and show that it gives…
The emergence of travelling sine-Gordon breathers due to the nonlinear supratransmission effect is theoretically studied in a long Josephson junction driven by suitable magnetic pulses, taking into account the presence of dissipation, a…
The development of superconducting electronics requires careful characterization of the components that make up electronic circuits. Superconducting weak links are the building blocks of most superconducting electronics components and are…
We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown…
In this thesis we deal with the specific collective phenomena in condensed matter - striped-structures formation. Such structures are observed in different branches of condensed matter physics, like surface physics or physics of…
Superinductors have become a crucial component in the superconducting circuit toolbox, playing a key role in the development of more robust qubits. Enhancing the performance of these devices can be achieved by suspending the superinductors…
In this communication, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of the model and connect it with earlier work on models including geometric effects. We focus on both the…
$q$-breathers are exact time-periodic solutions of extended nonlinear systems continued from the normal modes of the corresponding linearized system. They are localized in the space of normal modes. The existence of these solutions in a…
The existence of highly localized multi-site oscillatory structures (discrete multibreathers) in a nonlinear Klein-Gordon chain which is characterized by an inverse dispersion law is proven and their linear stability is investigated. The…