Related papers: Predicting instabilities of a tuneable ring laser …
We report a modulational instability (MI) analysis of a mathematical model appropriate for ultrashort pulses in cascaded quadratic-cubic nonlinear media beyond the so-called slowly varying envelope approximation. Theoretically predicted MI…
The main goal of this article is to study a Calder\'on type inverse problem for certain viscous nonlocal wave equations. We show that the partial Dirichlet to Neumann map uniquely determines on the one hand linear perturbations and on the…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
The choice of a suitable regularization parameter is an important part of most regularization methods for inverse problems. In the absence of reliable estimates of the noise level, heuristic parameter choice rules can be used to accomplish…
We deal with the orbit determination problem for a class of maps of the cylinder generalizing the Chirikov standard map. The problem consists of determining the initial conditions and other parameters of an orbit from some observations. A…
Spatio-temporal instabilities are widespread phenomena resulting from complexity and nonlinearity. In broad-area edge-emitting semiconductor lasers, the nonlinear interactions of multiple spatial modes with the active medium can result in…
Shear-thinning fluids flowing through pipes are crucial in many practical applications, yet many unresolved problems remain regarding their turbulent transition. Using highly robust numerical tools for the Carreau-Yasuda model, we…
We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show…
We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and…
The analysis of electrical impulse phenomena in cardiac muscle tissue is important for the diagnosis of heart rhythm disorders and other cardiac pathophysiology. Cardiac mapping techniques acquire local temporal measurements and combine…
The interaction between two co-propagating electrostatic wavepackets characterized by arbitrary carrier wavenumber is considered. A one-dimensional (1D) non-magnetized plasma model is adopted, consisting of a cold inertial ion fluid…
A stability analysis is made for a non-singular pre-big-bang like cosmological model based on 1-loop corrected string effective action. Its homogeneous and isotropic solution realizes non-singular transition from de Sitter universe to…
The aim of this paper is to clarify the stabilities of neutron stars with strong toroidal magnetic fields against non-axisymmetric perturbation. The motivation comes from the fact that super magnetized neutron stars of $\sim 10^{15}$G,…
We study evolution of pulses propagating through focusing nonlinear media. Small disturbance on the smooth initial non-uniform background leads to formation of the region of strong nonlinear oscillations. We develop here an asymptotic…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
This paper develops a computational method for studying stable/unstable manifolds attached to periodic orbits of differential equations. The method uses high order Chebyshev-Taylor series approximations in conjunction with the…
We study inverse boundary problems for semilinear Schr\"odinger equations on smooth compact Riemannian manifolds of dimensions $\ge 2$ with smooth boundary, at a large fixed frequency. We show that certain classes of cubic nonlinearities…
This paper proposes a robust lattice-based motion-planning algorithm for nonlinear systems affected by a bounded disturbance. The proposed motion planner utilizes the nominal disturbance-free system model to generate motion primitives,…
We report numerical and experimental investigations into modulation instability in a nonlinear magnetoinductive waveguide. By numerical simulation we find that modulation instability occurs in an electrical circuit model of a…
This study presents a nonlinear signal processing method for accurate radar-based heartbeat interval estimation by exploiting the periodicity of higher-order harmonics inherent in heartbeat signals. Unlike conventional approaches that…