where 2 < α ≤ 3, D denotes the Riemann-Liouville fractional derivative, λ is a positive constant, f (t, x) may change sign and be singular at t = 0, t = 1, and x = 0. By means of the Guo-Krasnoselskii fixed point theorem, the eigenvalue intervals of the nonlinear fractional functional differential equation boundary value problem are considered, and some positive solutions are obtained, respecti...

The soliton structure of a gauge theory proposed to describe chiral excitations in the multi-Layer Fractional Quantum Hall Effect is investigated. A new type of derivative multi-component nonlinear Schrödinger equation emerges as effective description of the system that supports novel chiral solitons. We discuss the classical properties of the solutions and study relations to integrable systems.

The one-dimensional oblique propagation of magnetohydrodynamic waves with arbitrary amplitudes in a Hall plasma with isotropic pressure is studied under assumption that the plasma β is large. It is shown that the wave evolution is described by the derivative nonlinear Schrödinger equation (DNLS).

In order to incorporate the credit value adjustment (CVA) in derivative contracts, we propose a set of numerical methods to solve a nonlinear partial differential equation [2] modelling the CVA. Additionally to adequate boundary conditions proposals, characteristics methods, fixed point techniques and finite elements methods are designed and implemented. A numerical test illustrates the behavio...

In this paper, we present some new variants of Chebyshev-Halley methods free from second derivative for solving nonlinear equation of the type f(x) = 0, and show that the convergence orders of the proposed methods are three or four. Several numerical examples are given to illustrate the efficiency and performance of the new methods.

The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered.The concept of variable order fractional derivative is considered in the sense of Caputo.The stability analysis and the truncation error of the method are discussed. To demonstrate the effectiveness of the method, some numerical test examples are presen...

In this paper we mainly study the Cauchy problem for the derivative nonlinear Schrödinger equation in d-dimension (d ≥ 2). We obtain some global well-posedness results with small initial data. The crucial ingredients are L e , L ∞,2 e type estimates, and inhomogeneous local smoothing estimate (L e estimate). As a by-product, the scattering results with small initial data are also obtained.

We prove the existence of at least one solution to a nonlinear second-order differential equation on the half-line, with the boundary conditions x′(0) = 0 and with the first derivative vanishing at infinity. Our main tool is the multi-valued version of the Miranda Theorem.

An explicit two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characte...

Absrtract. Group classification of systems of two coupled nonlinear reaction-diffusion equation with a general diffusion matrix started in papers [1], [2] is completed in present paper where all non-equivalent equations with triangular diffusion matrix are classified. In addition, symmetries of diffusion systems with nilpotent diffusion matrix and additional first order derivative terms are des...