A new approach to the Darboux-Bäcklund transformation versus the standard dressing method

Journal of Physics A: Mathematical and General

Volumn 38, Issue 43, 2005, Pages 9491-9501

  Cieśliński, Jan L ^a   Biernacki, Waldemar ^b  

^a UNIVERSITY OF BIALYSTOK   (Poland)

^b Katedra Informatyki ^*  (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 26844541622     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/43/006     Document Type: Article

References (19)

1. Zakharov V E and Shabat A B 1979 Integration of nonlinear equations of mathematical physics by the inverse scattering method. II Funk. Anal. Pril. 13 13-22 (in Russian)
2. Mikhailov A V 1981 The reduction problem and the inverse scattering method Physica D 3 73-117
3. Neugebauer G and Meinel R 1984 General N-soliton solution of the AKNS class on arbitrary background Phys. Lett. A 100 467-70
4. Its A R 1984 Liouville's theorem and the inverse scattering method Zapiski Nau. Sem. LOMI 133 113-25 (in Russian)
5. Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
6. Gu C H 1995 Bäcklund transformations and Darboux transformations Soliton Theory and Its Applications (Berlin: Springer) pp 122-51
7. Cieśliński J 1995 An algebraic method to construct the Darboux matrix J. Math. Phys. 36 5670-706
8. Rogers C and Schief W K 2002 Bäcklund and Darboux transformations: Geometry and Modern Applications in Soliton Theory (Cambridge: Cambridge University Press)
9. 3 as soliton surfaces Phys. Lett. A 205 37-43
10. Cieśliński J 1997 The Darboux-Bianchi transformation for isothermic surfaces. Classical results versus the soliton approach Diff. Geom. Appl. 7 1-28
11. Cieśliński J L 2000 A class of linear spectral problems in Clifford algebras Phys. Lett. A 267 251-5
12. Cieśliński J L 2003 Geometry of submanifolds derived from spin-valued spectral problems Theor. Math. Phys. 137 1396-405
13. Biernacki W and Cieśliński J L 2001 A compact formula for the Darboux-Bäcklund transformation for some spectral problems in Clifford algebras Phys. Lett. A 288 167-72
14. Zakharov V E, Manakov S V, Novikov S P and Pitaievsky L P 1980 Theory of Solitons (Moscow: Nauka) (in Russian)
15. Meinel R, Neugebauer G and Steudel H 1991 Solitonen. Nichtlineare Strukturen (Berlin: Academie Verlag) (in German)
16. Cieśliński J L 1998 The Darboux-Bianchi-Bäcklund transformation and soliton surfaces Nonlinearity and Geometry ed D Wójcik and J L Cieśliński (Warsaw: Polish Scientific Publishers PWN) pp 81-107
17. Lang S 1965 Algebra (Reading, MA: Addison-Wesley)
18. Cieśliński J L 1991 An effective method to compute N-soliton Darboux matrix and N-soliton surfaces J. Math. Phys. 32 2395-9
19. Cieśliński J L 2000 The Darboux-Bäcklund transformation without using a matrix representation J. Phys. A: Math. Gen. 33 L363-8