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Original Articles

Gauge Transformation and Reciprocal Link for (2+1)-Dimensional Integrable Field Systems

Pages 117-128 | Received 09 May 2005, Accepted 15 Aug 2005, Published online: 21 Jan 2013

References

  • Błaszak , M and Marciniak , K . 1994 . R-matrix approach to lattice integrable systems . J. Math. Phys. , 35 : 4661
  • Błaszak , M and Szablikowski , B M . 2002 . Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theory . J. Phys A: Math. Gen. , 35 : 10325 – 44 .
  • Błaszak , M and Szablikowski , B M . 2002 . Classical R-matrix theory of dispersionless systems: II. (2+1) dimension theory . J. Phys A: Math. Gen. , 35 : 10345 – 64 .
  • Błaszak , M and Szablikowski , B M . 2003 . From dispersionless to soliton systems via Weyl-Moyal-like deformations . J. Phys A: Math. Gen. , 36 : 12181 – 203 .
  • Błlaszak , M and Szum , A . 2001 . Lie algebraic approach to the construction of (2+1)-dimensional lattice-field and field integrable Hamiltonian equations . J. Math. Phys. , 35 : 4088 – 116 .
  • Błaszak , M , Szum , A and Prykarpatsky , A . 2001 . Central extension approach to integrable field and lattice-field systems in (2+1)-dimensions . Rep. Math. Phys. , 44 : 37 – 44 .
  • Konopelchenko , B G and Dubrovsky , V G . 1984 . Some new integrable nonlinear evolution equations in 2+1 dimensions . Phys. Lett. A , 102 : 15 – 17 .
  • Konopelchenko , B and Oevel , W . 1991 . “ Matrix Sato theory and integrable equations in 2+1 dimensions ” . In Nonlinear evolution equations and dynamical systems , Edited by: Boiti , M. , Martina , L. and Pempinelli , F. Singapore : World Scientific .
  • Konopelchenko , B G and Oevel , W . 1993 . An r-matrix approach to nonstandard classes of integrable equations . Publ. RIMS, Kyoto Univ. , 29 : 581 – 666 .
  • Li , L C . 1999 . Classical r-Matrices and Compatible Poisson Structures for Lax Equations in Poisson Algebras . Commun. Math. Phys. , 203 : 573 – 92 .
  • Oevel , W and Rogers , C . 1993 . Gauge transformations and reciprocal links in 2+1 dimensions . Rev. Math. Phys. , 5 : 299
  • Oevel , W and Strampp , W . 1993 . Constrained KP hierrachy and bi-Hamitonian structures . Commun. Math. Phys. , 157 : 51
  • Prykarpatsky , A K , Samoilenko , V Hr and Andrushkiw , R I . 1994 . Algebraic structure of the gradientholonomic algorithm for Lax integrable nonlinear dynamical systems I . J. Math. Phys. , 35 : 1763 – 77 .
  • Sato , M . Soliton equations as dynamical systems on infinite Grassmann manifold . RIMS Kokyuroku, Kyoto Univ. , 439 30
  • Semenov-Tian-Shansky , M A . 1983 . What is a classical r-matrix/ . Funct. Anal. Appl. , 17 : 259
  • Reyman , A G and Semenov-Tian-Shansky , M A . Current algebras and nonlinear partial differential equations, (in russian) . Dokl. Akad. nauk , 251 1310
  • Reyman , A G and Semenov-Tian-Shansky , M A . 1984 . Hamiltonian structure of Kadomtsev-Petviashvili type equations (in russian) . LOMI , 133 ( 6 ) : 212

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