Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System

Analytic-bilinear Approach to Integrable Hierarchies. Ii. Multicomponent Kp and 2d Toda Lattice Hierarchies

Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows to represent generalized hierarchies of integrable equations in a condensed form of finite functional equations. Generalized hierarchy incorporates basic hierarchy, modified hierarchy, singularity manifol...

Explicit solutions of supersymmetric KP hierarchies: Supersolitons and solitinos

Wide classes of explicit solutions of the Manin-Radul and Jacobian supersymmetric KP hierarchies are constructed by using line bundles over complex supercurves based on the Riemann sphere. Their construction extends several ideas of the standard KP theory, such as wave functions, ]̄-equations and t-functions. Thus, supersymmetric generalizations of N-soliton solutions, including a new purely odd...

KP and KdV hierarchies in extended superspace

We give the formulation in extended superspace of an N = 2 super-symmetric KP hierarchy using chirality preserving pseudo-differential operators. We obtain two quadratic hamiltonian structures, which lead to different reductions of the KP hierarchy. In particular we find two different hierarchies with the N = 2 classical super-W n algebra as a hamiltonian structure. The relation with the formul...

Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction properties of two-soliton solutions.

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations