Scattering theory for 4-th order differential operator, II

An existence result for n^{th}-order nonlinear fractional differential equations

In this paper, we investigate the existence of solutions of some three-point boundary value problems for n-th order nonlinear fractional differential equations with higher boundary conditions by using a fixed point theorem on cones.

Time Evolution of the Scattering Data for a Fourth-order Linear Differential Operator

The time evolution of the scattering and spectral data is obtained for the differential operator d dx4 + d dx u(x, t) d dx + v(x, t), where u(x, t) and v(x, t) are real-valued potentials decaying exponentially as x → ±∞ at each fixed t. The result is relevant in a crucial step of the inverse scattering transform method that is used in solving the initialvalue problem for a pair of coupled nonli...

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

Constrained Multivariable Operator Theory Ii

Broadband Spatiotemporal Differential-operator Representations for Velocity-dependent Scattering

A novel approach based on spatiotemporal differentialoperators is developed here for broadband, velocity-dependent scattering. Unlike the spectral-domain representations, the new method facilitates a compact formulation for scattering by arbitrary excitation signals, in the presence of moving objects. In free space (vacuum), relativistically exact formulas are developed. After developing the ge...