We study the possibility of obtaining large nongaussian signatures in the Cosmic Microwave Background in a general class of single-field nonlocal hill-top inflation models. We estimate the nonlinearity parameter fNL which characterizes nongaussianity in such models and show that large nongaussianity is possible. For the recently proposed p-adic inflation model we find that fNL ∼ 120 when the st...

A unified analytical description of the evolution of quasi-linear optical pulses and solitons in strongly dispersion-managed transmission systems is developed. Asymptotic analysis of the nonlocal equation that describes the averaged dynamics of a dispersion-managed system shows that the nonlinearity decreases for large map strength s , as O(log s/s) . The spectral intensity is found to be an in...

In this paper we prove that the steepest descent of certain porous-medium type functionals with respect to the quadratic Wasserstein distance over a constrained (but not weakly closed) manifold gives rise to a nonlinear, nonlocal parabolic partial differential equation connected to the study of the asymptotic behavior of solutions for filtration problems. The result by Carlen and Gangbo on cons...

We study a mixed–state Schrödinger–Poisson–Slater system (SPSS). This system combines the nonlinear and nonlocal Coulomb interaction with a local potential nonlinearity known as the ”Slater exchange term” which models a fermionic effect. The origin of the model is explained and related models are also proposed. Existence, uniqueness and regularity of local–in–time and global solutions are analy...

We consider the nonlinear Schrödinger systems −i∂tu1 + 1 2 ∆u1 = F (u1, u2), i∂tu2 + 1 2 ∆u2 = F (u1, u2) in n space dimensions, where F is a p-th order local or nonlocal nonlinearity smooth up to order p, with 1 < p ≤ 1 + 2 n for n ≥ 2 and 1 < p ≤ 2 for n = 1. These systems are related to higher order nonlinear dispersive wave equations. We prove the non existence of asymptotically free soluti...

This paper is devoted to the study of the travelling front solutions which appear in a nonlocal reaction-diffusion equations of the form ∂u ∂t = J ⋆ u− u+ f(u). When the nonlinearity f is of bistable or ignition type, and the dispersion kernel J is asymmetric, the existence of a travelling wave is proved. The uniqueness of the speed of the front is also established. The construction of the fron...

In our previous work the nonlinearity parameter fNL, which characterizes nongaussianity in the cosmic microwave background, was estimated for a class of inflationary models based on nonlocal field theory. These models include p-adic inflation and generically have the remarkable property that slow roll inflation can proceed even with an extremely steep potential. Previous calculations found that...

This work investigates the existence of multiple positive solutions for a system two nonlinear higher-order fractional differential equations with ϕ-Laplacian operators and nonlocal conditions. A degenerate nonlinearity which obeys some general growth conditions is considered. The singularities are dealt by approximating fixed point operator. New results presented using index theory. Examples a...