Uniqueness of the Kadomtsev-Petviashvili and Boussinesq Equations


MA W. , Pekcan A.

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, cilt.66, ss.377-382, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 66
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1515/zna-2011-6-701
  • Dergi Adı: ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
  • Sayfa Sayıları: ss.377-382

Özet

The Kadomtsev-Petviashvili and Boussinesq equations (u(xxx) - 6uu(x))(x) - u(tx) +/- u(yy) = 0, (u(xxx) - 6uu(x))(x) + u(xx) +/- u(tt) = 0, are completely integrable, and in particular, they possess the three-soliton solution. This article aims to expose a uniqueness property of the Kadomtsev-Petviashvili (KP) and Boussinesq equations in the integrability theory. It is shown that the Kadomtsev-Petviashvili and Boussinesq equations and their dimensional reductions are the only integrable equations among a class of generalized Kadomtsev-Petviashvili and Boussinesq equations (u(x1x1x1) - 6uu(x1))(x1) + Sigma(M)(i,j)=1a(ij)u(xixj) = 0, where the aij's are arbitrary constants and M is an arbitrary natural number, if the existence of the three-soliton solution is required.