We study a class of elliptic problems, involving $k$-Hessian and very fast-growing nonlinearity, on unit ball. prove the existence radial singular solution obtain its exact asymptotic behavior in neighborhood origin. Furthermore, we multiplicity regular solutions bifurcation diagrams. An essential ingredient this is analyzing number intersection points between for rescaled problems. In particul...

In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them to those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent experimental developments in the former context. The stability properties of the fundamental waves, for both onsite and intersite modes, are examined analytically and...

In this paper, the synthetic aperture radar (SAR) process of Hie ocean surface mapping is studied using a decomposition based on a Volterra model. By a mathematical expansion of the complex exponential of the complete SAR transform, these models decompose the nonlinear distortion mechanisms of the SAR spectrum over different spectra of polynomial interactions. Thus, they offer an alternative mo...

The universal method for testing linearity against smooth transition autoregressive (STAR) alternatives is the linearization of the STAR model around the null nuisance parameter value, and performing F-tests on polynomial regressions in the spirit of the RESET test. Polynomial regressors, however, are poor proxies for the nonlinearity associated with STAR processes, and are not consistent (asym...

We consider two noninteracting two-level emitters that are coupled weakly to a one-dimensional nonlinear waveguide. Due the Kerr-like nonlinearity, waveguide considered supports---in addition scattering continuum---a two-body bound state. As such, models bath with nontrivial mode structure. Solving time-dependent Schr\"odinger equation, radiation dynamics of emitters, initially prepared in thei...

In this paper, the focus is on absolute stability and input-to-state stability of the feedback interconnection of an infinite-dimensional linear system Σ and a nonlinearity Φ : dom(Φ) ⊂ Lloc(R+, Y ) → L 2 loc(R+, U), where dom(Φ) denotes the domain of Φ and U and Y (Hilbert spaces) denote the input and output spaces of Σ, respectively (see Figure 1, wherein v is an essentially bounded input sig...

The major goal of the present paper is to construct optical solitons Ginzburg–Landau equation including parabolic nonlinearity. Such an ultimate formally achieved with aid symbolic computation, a complex transformation, and Kudryashov exponential methods. Several numerical simulations are given explore influence coefficients nonlinear terms on dynamical features obtained solitons. To best autho...

We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello it is proved that the profile of the solutions differs from global solutions of a Liouville type equation only by a uniformly bounded term. The pre...