Darboux-Bäcklund Transformations for Spin-Valued Linear Problems
45
3. J. Cie´ sli´ nski, Lie symmetries as a tool to isolate integrable geometries, in Nonlinear Evolution
Equations and Dynamical System, ed. by M. Boiti, L. Martina, F. Pempinelli (World Scientific,
Singapore 1992), pp. 260–268
4. J. Cie´ sli´ nski, Non-local symmetries and a working algorithm to isolate integrable geometries.
J. Phys. A Math. Gen. 26, L267–L271 (1993)
5. J. Cie´ sli´ nski, Group interpretation of the spectral parameter in the case of nonhomogeneous,
nonlinear Schrödinger system. J. Math. Phys. 34, 2372–2384 (1993)
6. J.L. Cie´ sli´ nski, P. Goldstein, A. Sym, On integrability of the inhomogeneous Heisenberg
ferromagnet model: Examination of a new test. J. Phys. A Math. Gen. 27, 1645–1664 (1994)
7. D. Levi, Hierarchies of integrable equations obtained as non-isospectral (in x and t) deformations of the Schrödinger spectral problem. Phys. Lett. A 119, 453–456 (1987)
8. J. Cie´ sli´ nski, Algebraic representation of the linear problem as a method to construct the
Darboux-Bäcklund transformation. Chaos Solitons Fractals 5, 2303–2313 (1995)
9. J. Cie´ sli´ nski, An algebraic method to construct the Darboux matrix. J. Math. Phys. 36,
5670–5706 (1995)
10. J. Cie´ sli´ nski, D. Levi, A. Sym, Solitons on a Relativistic String. DF-INFN N.496, 13/1/86.
Preprint (1986)
11. J. Cie´ sli´ nski, An effective method to compute N-fold Darboux matrix and N-soliton surfaces.
J. Math. Phys. 32, 2395–2399 (1991)
12. J. Cie´ sli´ nski, Two solitons on a thin vortex filament. Phys. Lett. A 171, 323–326 (1992)
13. J.L. Cie´ sli´ nski, Algebraic construction of the Darboux matrix revisited. J. Phys. A Math. Theor.
42, 404003 (2009)
14. J.L. Cie´ sli´ nski, A. Kobus, Group interpretation of the spectral parameter. The case of
isothermic surfaces. J. Geom. Phys. 113, 28–37 (2017)
15. J.L. Cie´ sli´ nski, An orbit-preserving discretization of the classical Kepler problem. Phys. Lett.
A 370, 8–12 (2007)
16. J.L. Cie´ sli´ nski, B. Ratkiewicz, Energy-preserving numerical schemes of high accuracy for onedimensional Hamiltonian systems. J. Phys. A Math. Theor. 44, 155206 (2011)
17. D. Levi, L. Martina, P. Winternitz, Structure preserving discretizations of the Liouville equation
and their numerical tests. SIGMA 11, 080 (2015)
18. J. Vaz, R. da Rocha, An Introduction to Clifford Algebras and Spinors (Oxford University
Press, 2017)
19. A. Sym, Soliton surfaces and their application (Soliton geometry from spectral problems), in
Geometric Aspects of the Einstein Equations and Integrable Systems, ed. by R. Martini. Lecture
Notes in Physics, vol. 239 (Springer, Berlin–Heidelberg, 1985), pp. 154–231
20. J.L. Cie´ sli´ nski, Geometry of submanifolds derived from spin-valued spectral problems. Theor.
Math. Phys. 137, 1396–1405 (2003)
21. P. Lounesto, Clifford Algebras and Spinors, 2nd edn. (Cambridge University Press, Cambridge,
2001)
22. F.E. Burstall, Isothermic surfaces: conformal geometry, Clifford algebras and integrable
systems, in Integrable systems, Geometry and Topology, ed. by C.-L. Terng. AMS/IP Studies
in Advanced Math., vol. 36, pp. 1–82 (2006)
23. J.L. Cie´ sli´ nski, A class of spectral problems in Clifford algebras. Phys. Lett. A 267, 251–255
(2000)
24. S.P. Novikov, S.V. Manakov, L.P. Pitaievsky, V.E. Zakharov, Theory of Solitons (Springer US,
New York, 1984)
25. C.H. Gu, Bäcklund transformations and Darboux transformations, in Soliton Theory and Its
Applications, ed. by C.H. Gu. (Springer, Berlin–Heidelberg, 1995), pp. 122–151
26. A.V. Mikhailov, The reduction problem and the inverse scattering method. Physica D 3, 73–117
(1981)
27. G. Neugebauer, R. Meinel, General N-soliton solution of the AKNS class on arbitrary
background. Phys. Lett. A 100, 467–470 (1984)
28. C. Rogers, W.K. Schief, Bäcklund and Darboux Transformations: Geometry and Modern
Applications in Soliton Theory (Cambridge University Press, Cambridge, 2002)
45
3. J. Cie´ sli´ nski, Lie symmetries as a tool to isolate integrable geometries, in Nonlinear Evolution
Equations and Dynamical System, ed. by M. Boiti, L. Martina, F. Pempinelli (World Scientific,
Singapore 1992), pp. 260–268
4. J. Cie´ sli´ nski, Non-local symmetries and a working algorithm to isolate integrable geometries.
J. Phys. A Math. Gen. 26, L267–L271 (1993)
5. J. Cie´ sli´ nski, Group interpretation of the spectral parameter in the case of nonhomogeneous,
nonlinear Schrödinger system. J. Math. Phys. 34, 2372–2384 (1993)
6. J.L. Cie´ sli´ nski, P. Goldstein, A. Sym, On integrability of the inhomogeneous Heisenberg
ferromagnet model: Examination of a new test. J. Phys. A Math. Gen. 27, 1645–1664 (1994)
7. D. Levi, Hierarchies of integrable equations obtained as non-isospectral (in x and t) deformations of the Schrödinger spectral problem. Phys. Lett. A 119, 453–456 (1987)
8. J. Cie´ sli´ nski, Algebraic representation of the linear problem as a method to construct the
Darboux-Bäcklund transformation. Chaos Solitons Fractals 5, 2303–2313 (1995)
9. J. Cie´ sli´ nski, An algebraic method to construct the Darboux matrix. J. Math. Phys. 36,
5670–5706 (1995)
10. J. Cie´ sli´ nski, D. Levi, A. Sym, Solitons on a Relativistic String. DF-INFN N.496, 13/1/86.
Preprint (1986)
11. J. Cie´ sli´ nski, An effective method to compute N-fold Darboux matrix and N-soliton surfaces.
J. Math. Phys. 32, 2395–2399 (1991)
12. J. Cie´ sli´ nski, Two solitons on a thin vortex filament. Phys. Lett. A 171, 323–326 (1992)
13. J.L. Cie´ sli´ nski, Algebraic construction of the Darboux matrix revisited. J. Phys. A Math. Theor.
42, 404003 (2009)
14. J.L. Cie´ sli´ nski, A. Kobus, Group interpretation of the spectral parameter. The case of
isothermic surfaces. J. Geom. Phys. 113, 28–37 (2017)
15. J.L. Cie´ sli´ nski, An orbit-preserving discretization of the classical Kepler problem. Phys. Lett.
A 370, 8–12 (2007)
16. J.L. Cie´ sli´ nski, B. Ratkiewicz, Energy-preserving numerical schemes of high accuracy for onedimensional Hamiltonian systems. J. Phys. A Math. Theor. 44, 155206 (2011)
17. D. Levi, L. Martina, P. Winternitz, Structure preserving discretizations of the Liouville equation
and their numerical tests. SIGMA 11, 080 (2015)
18. J. Vaz, R. da Rocha, An Introduction to Clifford Algebras and Spinors (Oxford University
Press, 2017)
19. A. Sym, Soliton surfaces and their application (Soliton geometry from spectral problems), in
Geometric Aspects of the Einstein Equations and Integrable Systems, ed. by R. Martini. Lecture
Notes in Physics, vol. 239 (Springer, Berlin–Heidelberg, 1985), pp. 154–231
20. J.L. Cie´ sli´ nski, Geometry of submanifolds derived from spin-valued spectral problems. Theor.
Math. Phys. 137, 1396–1405 (2003)
21. P. Lounesto, Clifford Algebras and Spinors, 2nd edn. (Cambridge University Press, Cambridge,
2001)
22. F.E. Burstall, Isothermic surfaces: conformal geometry, Clifford algebras and integrable
systems, in Integrable systems, Geometry and Topology, ed. by C.-L. Terng. AMS/IP Studies
in Advanced Math., vol. 36, pp. 1–82 (2006)
23. J.L. Cie´ sli´ nski, A class of spectral problems in Clifford algebras. Phys. Lett. A 267, 251–255
(2000)
24. S.P. Novikov, S.V. Manakov, L.P. Pitaievsky, V.E. Zakharov, Theory of Solitons (Springer US,
New York, 1984)
25. C.H. Gu, Bäcklund transformations and Darboux transformations, in Soliton Theory and Its
Applications, ed. by C.H. Gu. (Springer, Berlin–Heidelberg, 1995), pp. 122–151
26. A.V. Mikhailov, The reduction problem and the inverse scattering method. Physica D 3, 73–117
(1981)
27. G. Neugebauer, R. Meinel, General N-soliton solution of the AKNS class on arbitrary
background. Phys. Lett. A 100, 467–470 (1984)
28. C. Rogers, W.K. Schief, Bäcklund and Darboux Transformations: Geometry and Modern
Applications in Soliton Theory (Cambridge University Press, Cambridge, 2002)