We propose a new test based on a Fourier series to approximate the unknown form of a nonlinear time-series model. The test has good size and power properties to detect structural breaks, seasonal parameters and random coefficients. Moreover, it has reasonable power to discriminate between nonlinearity in variables and nonlinearity in parameters. We use the test to show that U.S. inflation is ap...

This paper studies the Biswas-Milovic equation with log law nonlinearity. The Gausson solution is obtained by the ansatz method. Subsequently, the conservation laws are derived and the conserved quantities are computed using the Gausson solution.

The biharmonic supercritical equation ∆u = |u|p−1u, where n > 4 and p > (n + 4)/(n − 4), is studied in the whole space R as well as in a modified form with λ(1 + u) as right-hand-side with an additional eigenvalue parameter λ > 0 in the unit ball, in the latter case together with Dirichlet boundary conditions. As for entire regular radial solutions we prove oscillatory behaviour around the expl...

We study the Cauchy problem for Schrödinger equations with repulsive quadratic potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the no...

The Talbot-Plateau law fails for flicker detected by the short-wavelength-sensitive (S) cones: a 30-40 Hz target, flickering too fast for the flicker to be resolved, looks more yellow than a steady target of the same average intensity. The color change, which is produced by distortion at an early compressive nonlinearity, was used to reveal a slightly bandpass S-cone temporal response before th...

We study the Cauchy problem for Schrödinger equations with repulsive quadratic potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the no...

In this paper, random walks with independent steps distributed according to a Q-power-law probability distribution function with Q=1/(1-q) are studied. In the case q>1, we show that (i) a stochastic representation of the location of the walk after n steps can be explicitly given (for both finite and infinite variance) and (ii) a clear connection with the superstatistics framework can be establi...