In this paper, we are concerned with the integrable decomposition for (2+1)-dimensional Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy. By utilizing recursive relations and symmetric reductions, propose that (n2 − n1 + 1)-flow of AKNS hierarchy can be decomposed into corresponding n1-flow n2-flow (1+1)-dimensional hierarchy, both in coupled reduced cases. As an appropriate generalization, decompos...

Stokes’ manifolds, also known as wild character varieties, carry a natural Poisson structure. Our goal is to provide explicit log-canonical coordinates for this structure on the manifolds of polynomial connections rank 2, thus including second Painlevé hierarchy. This construction provides linearization first discovered by Flaschka and Newell then rediscovered generalized Boalch. We show that, ...

In this study, we introduced a novel scheme to attain approximate and closed-form solutions of conformable Newell-Whitehead-Segel (NWS) equations, which belong the most consequential amplitude equations in physics. The Shehu transform (CST) Adomian decomposition method (ADM) are combined proposed method. We call it (CSDM). To assess efficiency consistency recommended method, demonstrate 2D 3D g...

The rational solutions of the Painlevé-II equation appear in several applications and are known to have many remarkable algebraic and analytic properties. They also have several different representations, useful in different ways for establishing these properties. In particular, Riemann–Hilbert representations have proven to be useful for extracting the asymptotic behavior of the rational solut...

While action potentials are the usual means of transmission in axons, recent work has established that decrementally conducted potentials are also utilized. Decremental conduction has been demonstrated to be the exclusive mode of transmission in certain sensory axons of vertebrates (Werblin & Dowling, 1969; Kaneko, 1967, 1970) and invertebrates (Gwilliam, 1965, Ripley, Bush & Roberts, 1968; Ioa...

In the early 1950s, as calculating machines were coming into their own, a few pioneer thinkers began to realize that digital computers could be more than number crunchers. At that point two opposed visions of what computers could be, each with its correlated research program, emerged and struggled for recognition. One faction saw computers as a system for manipulating mental symbols; the other,...

Why games? How could anyone consider action games as experimental paradigms for Cognitive Science? In 1973, as one of three strategies he proposed for advancing Cognitive Science, Allen Newell exhorted us to “accept a single complex task and do all of it.” More specifically, he told us that rather than taking an “experimental psychology as usual approach” that, we should “focus on a series of e...

The variations in total relative angular momentum of the atmosphere are examined for annual and shorter time scales. Use of a 5 year data set consisting of zonally-averaged values from the NMC twice daily analysis allows the construction of 2-dimensional (latitude-height) descriptions of the phenomena. Spatially coherent patterns have been identified associated with annual, semi-annual, and 40-...

Why games? How could anyone consider action games an experimental paradigm for Cognitive Science? In 1973, as one of three strategies he proposed for advancing Cognitive Science, Allen Newell exhorted us to "accept a single complex task and do all of it." More specifically, he told us that rather than taking an "experimental psychology as usual approach," we should "focus on a series of experim...