In this chapter, we perform six sets of experiments to evaluate the effectiveness of the APCDM and its submodels and their respective sensitivities to various parameters. First, we examine the performance of our stochastic approach towards generating aircraft trajectory realizations and conducting the overall conflict analysis. In addition to testing several probabilistic trajectory displacemen...

Interest in studying nonlinear models has been increasing recent years. Dynamical systems, which the state of system changes continuously over time, have interactions. The use unique differential equations is inescapable evaluation such systems. In mathematical point view, for obtaining analytical solutions equations, it must be fully integrable. Consequently, importance integrable science becom...

An equation describing particles with spin 3/2 is derived. This equation can be considered as " square root " of the Proca equation in the same sense as the Dirac equation is related to the Klein-Gordon-Fock equation. The equation considered involves fields with spin-3/2 and spin-1/2 (one copy), i.e. multi-spin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and...

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...

In this paper we will generalize a singular value inequality that was proved before. In particular we obtain an inequality for numerical radius as follows: begin{equation*} 2 sqrt{t (1-t)} omega(t A^{nu}B^{1-nu}+(1-t)A^{1-nu}B^{nu}) leq omega(t A + (1- t) B), end{equation*} where, $ A $ and $ B $ are positive semidefinite matrices, $ 0 leq t leq 1 $ and $ 0 leq nu leq frac{3}{2}.$

In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota’s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented. Keywords—three-wave method; (3+1)-dimensional Soliton equation; Hirota’s bilinear form.