منابع مشابه
Twistor Solutions of the dKP Equation ∗
The factorization problem for the group of canonical transformations close to the identity and the corresponding twistor equations for an ample family of canonical variables are considered. A method to deal with these reductions is developed for the construction classes of nontrivial solutions of the dKP equation.
متن کامل2 On Twistor Solutions of the dKP Equation ∗
The factorization problem for the group of canonical transformations close to the identity and the corresponding twistor equations for an ample family of canonical variables are considered. A method to deal with these reductions is developed for the construction classes of nontrivial solutions of the dKP equation.
متن کاملEinstein–Weyl geometry, the dKP equation and twistor theory
It is shown that Einstein–Weyl (EW) equations in 2+1 dimensions contain the dispersionless Kadomtsev–Petviashvili (dKP) equation as a special case: If an EW structure admits a constant weighted vector then it is locally given by h = dy2−4dxdt−4udt2, ν = −4uxdt, where u = u(x, y, t) satisfies the dKP equation (ut − uux)x = uyy. Linearised solutions to the dKP equation are shown to give rise to f...
متن کاملTwistor Theory of the Airy Equation
We demonstrate how the complex integral formula for the Airy functions arises from Penrose’s twistor contour integral formula. We then use the Lax formulation of the isomonodromy problem with one irregular singularity of order four to show that the Airy equation arises from the anti-self-duality equations for conformal structures of neutral signature invariant under the isometric action of the ...
متن کاملN-soliton Solutions to the Dkp Equation and Weyl Group Actions
where τ0 = 1. The τ -functions τn are given by the pfaffians of certain skew-symmetric matrix. We identify one-soliton solution as an element of the Weyl group of D-type, and discuss a general structure of the interaction patterns among the solitons. Soliton solutions are characterized by 4N × 4N skew-symmetric constant matrix which we call the B-matrices. We then find that one can have M -soli...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2003
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/36/23/311