We establish a relation between the classical non-linear Schrödinger equation and the KP hierarchy, and we extend this relation to the quantum case by defining a quantum KP hierarchy. We also present evidence that an integrable hierarchy of equations is obtained by quantizing the first Hamiltonian structure of the KdV equation. The connection between infinite-dimensional algebras and integrable...

We show that the Manin-Radul super KP hierarchy is invariant under super W ∞ transformations. These transformations are characterized by time dependent flows which commute with the usual flows generated by the conserved quantities of the super KP hierarchy.

We develop the symbolic representation method to derive the hierarchies of (2+1)-dimensional integrable equations from the scalar Lax operators and to study their properties globally. The method applies to both commutative and noncommutative cases in the sense that the dependent variable takes its values in C or a noncommutative associative algebra. We prove that these hierarchies are indeed qu...

We give a determinantal formula for tau functions of the KP hierarchy in terms of rectangular constant matrices A, B, and C satisfying a rank-one condition. This result is shown to generalize and unify many previous results of different authors on constructions of tau functions for differential and difference integrable systems from square matrices satisfying rank-one conditions. In particular,...

Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili [Kadomtsev BB, Petviashvili VI (1970) Sov Phys Dokl 15:539-541] proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solution...

Several studies have shown that visual recovery after blindness that occurs early in life is never complete. The current study investigated whether an extremely long period of blindness might also cause a permanent impairment of visual performance, even in a case of adult-onset blindness. We examined KP, a 71-year-old man who underwent a successful sight-restoring operation after 53 years of bl...

An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered he...

Background. Skin diseases among pediatric patients differ from those in adults. Epidemiological studies are scarce, and those performed in Mexican population date back thirty years. It is likely that these diseases might have changed their frequency. Material and Methods. Retrospective study in first-time patients referred to a pediatric dermatology service between January 1994 and December 200...

Pityriasis rubra pilaris (PRP) is a rare chronic inflammatory keratosis that is clinically characterized by gradually developing reddish or orange extending plaques and keratotic follicular papules. In pediatric patients, we frequently hesitate to administer certain medications for treatment of PRP, specifically etretinate, systemic corticosteroids, and biologics recommended by previous studies...

Tyrosine kinase enzymes are an attractive target for anticancer therapies. Tyrosine kinase inhibitors (TKI) are well tolerated; somehow severe systemic side effects are rarely seen during treatment. Toxicities of skin and appendages may lead to poor compliance, psychosocial inconvenience, and drug interruption. Changes of the hair can arise following cures with TKI. Nilotinib, a second-generati...