Related papers: A corresponding relationship between nonlinear Her…
We numerically determine the robustness of the lasing edge modes in a spin-torque oscillator array that realizes the non-Hermitian Su-Schrieffer-Heeger model. Previous studies found that the linearized dynamics can enter a topological…
We study optomechanical interactions in non-Hermitian photonic molecules that support two photonic states and one acoustic mode. The nonlinear steady-state solutions and their linear stability landscapes are investigated as a function of…
Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry$^{\dagger}$ (TRS$^{\dagger}$),…
Effects of nonlinear dynamics of solitary waves and wave modulations within the modular (also known as quadratically cubic) Korteweg - de Vries equation are studied analytically and numerically. Large wave events can occur in the course of…
Advances in topological photonics and non-Hermitian optics have drastically changed our perception on how interdisciplinary concepts may empower unprecedented applications. Bridging the two areas could uncover the reciprocity between…
We give a natural notion of nondegeneracy for singular points of integrable non-Hamiltonian systems, and show that such nondegenerate singularities are locally geometrically linearizable and deformation rigid in the analytic case. We…
The recent progress in the context of elastic metamaterials and modulated waveguides with digitally controllable properties has opened new pathways to overcome the limitations dictated by Hermitian Hamiltonians in mechanics. Among the…
We revisit the Swift-Hohenberg model for two-dimensional hexagonal patterns in the bistability region where hexagons coexist with the uniform quiescent state. We both analyze the law of motion of planar interfaces (separating hexagons and…
The bulk-boundary correspondence predicts the existence of boundary modes localized at the edges of topologically nontrivial systems. The wavefunctions of hermitian boundary modes can be obtained as the eigenmodes of a modified Jackiw-Rebbi…
We study the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, the diagonal matrix elements of which are random complex variables taking both positive (loss) and negative (gain) imaginary values: Their…
A full theory for hinged beams and degenerate plates with multiple intermediate piers is developed. The analysis starts with the variational setting and the study of the linear stationary problem in one dimension. Well-posedness results are…
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's…
We analyze the dynamics of modulation instability in optical fiber (or any other nonlinear Schr\"{o}dinger equation system) using the machine-learning technique of data-driven dominant balance. We aim to automate the identification of which…
We investigate the dissipative dynamics of linear and nonlinear waves in harmonic traps by means of engineered complex non-Hermitian potentials. By combining an analytical mapping between real and complex Schr\"odinger equations with direct…
Eigenvalues and eigenvectors of non-Hermitian tridiagonal periodic random matrices are studied by means of the Hatano-Nelson deformation. The deformed spectrum is annular-shaped, with inner radius measured by the complex Thouless formula.…
In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time…
The long-time asymptotic behavior of solutions to the focusing nonlinear Schr\"odinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the case of initial conditions that allow for the…
An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
Time-independent scattering methods are widely employed to analyze transport in non-Hermitian systems. Their application, however, rests on a critical yet often overlooked assumption: that an incident wave is a pure superposition of…