Darboux operators for linear first-order multi-component equations in arbitrary dimensions

• Authors: Axel Schulze-Halberg
• Languages of publication: EN

Abstracts

EN

We construct Darboux operators for linear, multi-component partial differential equations of first order. The number of variables and the dimension of the matrix coefficients in our equations are arbitrary. The Darboux operator and the transformed equation are worked out explicitly. We present an application of our formalism to the (1+2)-dimensional Weyl equation.

Keywords

EN

Darboux operator; multi-component differential equation; intertwining relation

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 4
• Pages: 457-469

Dates

published

1 - 4 - 2013

online

22 - 5 - 2013

Contributors

author

Axel Schulze-Halberg

• Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN, 46408, USA

References

• [1] G. Darboux, Comptes Rendus Acad. Sci. Paris 94, 1456 (1882)
• [2] C. Gu, H. Hu, Z. Zhou, Darboux transformations in integrable systems, Mathematical Physics Studies 26 (Springer, Dordrecht, The Netherlands, 2005)
• [3] V.B. Matveev, M.A. Salle, Darboux transformations and solitons (Springer, Berlin, 1991) http://dx.doi.org/10.1007/978-3-662-00922-2[Crossref]
• [4] V.G. Bagrov, B.F. Samsonov, Phys. Lett. A 210, 60 (1996) http://dx.doi.org/10.1016/0375-9601(95)00832-2[Crossref]
• [5] F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995) http://dx.doi.org/10.1016/0370-1573(94)00080-M[Crossref]
• [6] D.J. Fernandez, AIP Conference Proceedings 1287, 3 (2010)
• [7] A. Anderson, Phys. Rev. A 43, 4602 (1991) http://dx.doi.org/10.1103/PhysRevA.43.4602[Crossref]
• [8] B.F. Samsonov, V.V. Shamshutdinova, J. Phys. A 38, 4715 (2005) http://dx.doi.org/10.1088/0305-4470/38/21/015[Crossref]
• [9] A. Contreras, D.J. Fernandez C., J. Negro, SIGMA 8, 082 (2012)
• [10] N. Debergh, A.A. Pecheritsin, B.F. Samsonov, B. van den Bossche, J. Phys. A 35, 3279 (2002) http://dx.doi.org/10.1088/0305-4470/35/14/309[Crossref]
• [11] L.M. Nieto, A. A. Pecheritsin, B.F. Samsonov, Ann. Phys. 305, 151 (2003) http://dx.doi.org/10.1016/S0003-4916(03)00071-X[Crossref]
• [12] E. Pozdeeva, Int. J. Mod. Phys. A 23, 247 (2008) http://dx.doi.org/10.1142/S0217751X08038500[Crossref]
• [13] E. Pozdeeva, A. Schulze-Halberg, J. Math. Phys. 51, 113501 (2010) http://dx.doi.org/10.1063/1.3505127[Crossref]
• [14] A.V. Yurov, Phys. Lett. A 225, 51 (1997) http://dx.doi.org/10.1016/S0375-9601(96)00836-5[Crossref]
• [15] B. Blanes, F. Casas, J.A. Oteo, J. Ros, Phys. Rep. 470, 151 (2009) http://dx.doi.org/10.1016/j.physrep.2008.11.001[Crossref]

Identifiers

DOI

10.2478/s11534-013-0242-0