Related papers: Neutral delay differential equation Kerr cavity mo…
The spacelike reduction of the Chern-Simons Lagrangian yields a modified Nonlinear Schr\"odinger Equation (jNLS) where in the non-linearity the particle density is replaced by current. When the phase is linear in the position, this latter…
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…
A model for a non-Kerr cylindrical nematic fiber is presented. We use the multiple scales method to show the possibility of constructing different kinds of wavepackets of transverse magnetic (TM) modes propagating through the fiber. This…
We derive a (1+1)-dimensional nonlinear evolution equation (NLE) which may model the propagation of high-frequency perturbations in a relaxing medium. As a result, this equation may possess three typical solutions depending on a dissipative…
The spacelike reduction of the Chern-Simons Lagrangian yields a modified Nonlinear Schr\"odinger Equation (jNLS) where in the non-linearity the particle density is replaced by current. When the phase is linear in the position, this latter…
We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…
It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian $L(F)$, $F = F_mn F^mn$ having a correct weak field limit, leads to nontrivial static, spherically symmetric solutions with a globally…
We consider a class of particular solutions to the (2+1)-dimensional nonlinear partial differential equation (PDE) $u_t +\partial_{x_2}^n u_{x_1} - u_{x_1} u =0$ (here $n$ is any integer) reducing it to the ordinary differential equation…
An integrable model possessing inhomogeneous ground states is proposed as an effective model of non-uniform quantum condensates such as supersolids and Fulde--Ferrell--Larkin--Ovchinnikov superfluids. The model is a higher-order analog of…
We present a general approach to excite robust dissipative three-dimensional and high-order solitons and breathers in passively driven nonlinear cavities. Our findings are illustrated in the paradigmatic example provided by an optical Kerr…
We demonstrate the existence of breathing dissipative light bullets in a birefringent optical resonator filled with Kerr media. The propagation of light inside the cavity for each polarized component, which is coupled by cross-phase…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…
N-dark-dark solitons in the generally coupled integrable NLS equations are derived by the KP-hierarchy reduction method. These solitons exist when nonlinearities are all defocusing, or both focusing and defocusing nonlinearities are mixed.…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
The Kerr solution is defined by a null congruence which is geodesic and shear free and has a singular line contained in a bounded region of space. A generalization of the Kerr congruence for nonstationary case is obtained. We find a…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by generalizing the ideas introduced for the KdV…
An inverse-free neural network model with mixed delays is proposed for solving the absolute value equation (AVE) $Ax -|x| - b =0$, which includes an inverse-free neural network model with discrete delay as a special case. By using the…
We analyse the nonlinear dynamics of Fabry-Perot cavities of arbitrary finesse filled by a dispersive Kerr medium, pumped by a continuous wave laser or a synchronous train of flat-top pulses. The combined action of feedback, group velocity…
The goal of this paper is to provide a geometric framework for analyzing the uniform decay properties of solutions to the Teukolsky equation in the fully nonlinear setting of perturbations of Kerr. It contains the first nonlinear version of…