N-soliton Solutions to the Dkp Equation and Weyl Group Actions
نویسنده
چکیده
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 -soliton solutions with M being any number from N to 2N−1 for some of the 4N×4N B-matrices having only 2N nonzero entries in the upper triangular part (the number of solitons obtained from those B-matrices was previously expected to be just N).
منابع مشابه
Se p 20 02 Einstein – Weyl spaces and dispersionless Kadomtsev – Petviashvili equation from Painlevé I and II .
We present two constructions of new solutions to the dispersionless KP (dKP) equation arising from the first two Painlevé transcendents. The first construction is a hodograph transformation based on Einstein–Weyl geometry, the generalised Nahm's equation and the isomonodromy problem. The second construction, motivated by the first, is a direct characterisation of solutions to dKP which are cons...
متن کاملEinstein–weyl Spaces and Dispersionless Kadomtsev–petviashvili Equation from Painlevé I and Ii
We present two constructions of new solutions to the dispersionless KP (dKP) equation arising from the first two Painlevé transcendents. The first construction is a hodograph transformation based on Einstein–Weyl geometry, the generalised Nahm's equation and the isomonodromy problem. The second construction, motivated by the first, is a direct characterisation of solutions to dKP which are cons...
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 کاملMulti-soliton of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation and KdV equation
A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...
متن کاملExplicit multiple singular periodic solutions and singular soliton solutions to KdV equation
Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...
متن کامل