The quaternionic KP hierarchy is the integrable hierarchy of p.d.e obtained by replacing the complex numbers with the quaternions in the standard construction of the KP hierarchy and its solutions; it is equivalent to what is often called the Davey-Stewartson II hierarchy. This article studies its relationship with the theory of conformally immersed tori in the 4-sphere via quaternionic holomor...

We prove that the KP-I initial-value problem { ∂tu+ ∂ 3 xu− ∂ x ∂ yu+ ∂x(u/2) = 0 on Rx,y × Rt; u(x, y, 0) = φ(x, y), is locally well-posed in the space H(R) = {φ ∈ L(R) : ‖φ‖H1,0(R2) ≈ ‖φ‖L2 + ‖∂xφ‖L2 < ∞}.

We consider N-soliton solutions of the KP equation, (−4ut + uxxx + 6uux)x + 3uyy = 0 . An N-soliton solution is a solution u(x, y, t) which has the same set of N line soliton solutions in both asymptotics y → ∞ and y → −∞. The N-soliton solutions include all possible resonant interactions among those line solitons. We then classify those N-soliton solutions by defining a pair of N-numbers (n,n)...

We use the representation theory of the infinite matrix group to show that (in the polynomial case) the n–vector k–constrained KP hierarchy has a natural geometrical interpretation on Sato’s infinite Grassmannian. This description generalizes the the k–reduced KP or Gelfand–Dickey hierarchies.

We consider the nonstandard constrained KP (ncKP) hierarchy which is obtained from the multi-constraint KP hierarchy by gauge transformation. The second Hamiltonian structure of the ncKP hierarchy can be simplified by factorizing the Lax operator into multiplication form, thus the generalized Miura transformation is obtained. We also discuss the free field realization of the associated W-algebra.

The set of all rational functions with any fixed denominator that simultaneously nullify in the infinite point is parametrized by means of a well-known integrable system: a finite dimensional version of the discrete KP hierarchy. This type of study was originated in Y. Nakamura’s works who used others integrable systems. Our work proves that the finite discrete KP hierarchy completely parametri...

BACKGROUND Keratosis pilaris (KP) is a keratinization disorder that is characterized by follicular hyperkeratosis, with surrounding erythema. Topical treatments are widely used, but their effects are limited. OBJECTIVE To evaluate the effectiveness of the Q-switched 1064-nm Nd:YAG laser for the treatment of KP. METHODS Total of 12 patients with KP were treated with a Q-switched 1064-nm Nd:Y...

Objectives. To evaluate and compare the efficacy, safety, hydrating properties, and tolerability of 10% lactic acid (LA) and 5% salicylic acid (SA) in the therapy of keratosis pilaris (KP). Material and Method. Patients with KP were randomized for treatment with either 10% LA or 5% SA creams being applied twice daily for 3 months. The patients were clinically assessed at baseline and after 4, 8...

We consider an operator of Bernstein for symmetric functions, and give an explicit formula for its action on an arbitrary Schur function. This formula is given in a remarkably simple form when written in terms of some notation based on the code of a partition. As an application, we give a new and very simple proof of a classical result for the KP hierarchy, which involves the Plücker relations ...

Using Bäcklund transformation the spectral property of the KP-I lump solution is completely analyzed. It is proved that the lump solution is nondegenerate and has Morse index one. As a consequence we show that it is orbitally stable.