Publications of Adam Doliwa

  1. A. Doliwa and A. Sym, On Kida class of vortex filament motion, [in:] Symmetries in Science III, B. Gruber and S. Iachello (eds.), pp. 389-398, Plenum Press, New York 1989.

  2. A. Doliwa and A. Sym, Constant mean curvature helicoids in E3 as an example of soliton surfaces, [in:] Nonlinear Evolution Equations and Dynamical Systems, M. Boiti, L. Martina and F. Pompinelli (eds.), pp. 111-117, World Scientific, Singapore 1992.

  3. A. Doliwa and A. Sym, Minimal surfaces in S2m and Toda Systems, Warsaw University preprint No. IFT 11/92.

  4. A. Doliwa and P.M. Santini, An elementary geometric characterization of the integrable motions of a curve, Phys. Lett. A 185 (1994) 373-384, doi: 10.1016/0375-9601(94)90170-8.

  5. A. Doliwa and A. Sym, Non-linear sigma models on spheres and Toda systems, Phys. Lett. A 185 (1994) 453-460, doi: 10.1016/0375-9601(94)91125-8.

  6. A. Doliwa and P.M. Santini, Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy, J. Math. Phys. 36 (1995) 1259-1273, doi:10.1063/1.531119.

  7. A. Doliwa, What distinguishes soliton equations from other partial differential equations?, [in:] Bulletin of the Nonlinear Physics Research Group, No. 1, P. Goldstein, M. Pycia and D. Wójcik (eds.), pp. 28-35, A. Graf. UW, Warszawa 1995.

  8. A. Doliwa and P.M. Santini, The integrable dynamic of a discrete curve, [in:] Symmetries and Integrability of Difference Equations, D. Levi, L. Vinet and P. Winternitz (eds.), pp. 91-102, AMS, Providence 1996.

  9. A. Doliwa, Teoria solitonów i geometria, [in:] Fizyka teoretyczna lat 90-tych, P. Klimczewski and S.G. Rohoziński (eds.), pp. 41-53, Z. Graf. UW, Warszawa 1996.

  10. A. Doliwa, Harmonic maps and Toda systems, J. Math. Phys. 38 (1997) 1685-1691, doi:10.1063/1.531822.

  11. A. Doliwa, Holomorphic curves and Toda systems, Lett. Math. Phys. 39 (1997) 21-32, doi: 10.1007/s11005-997-1032-7.

  12. M. Mañas, A. Doliwa and P.M. Santini, Darboux transformations for multidimensional quadrilateral lattices. I, Phys. Lett. A 232 (1997) 99-105, doi: 10.1016/S0375-9601(97)00341-1.

  13. A. Doliwa and P.M. Santini, Multidimensional quadrilateral lattices are integrable, Phys. Lett. A 233 (1997) 365-372, doi: 10.1016/S0375-9601(97)00456-8.

  14. A. Doliwa, Geometric discretisation of the Toda system, Phys. Lett. A 234 (1997) 187-192, doi: 10.1016/S0375-9601(97)00477-5.

  15. J. Cieśliński, A. Doliwa and P.M. Santini, The integrable discrete analogues of orthogonal coordinate systems are multidimensional circular lattices, Phys. Lett. A 235 (1997) 480-488, doi: 10.1016/S0375-9601(97)00657-9.

  16. A. Doliwa, S.V. Manakov and P.M. Santini, D-bar reductions of the multidimensional quadrilateral lattice: the multidimensional circular lattice, Comm. Math. Phys. 196 (1998) 1-18, doi: 10.1007/s002200050411.

  17. A. Doliwa, Minimal surfaces, holomorphic curves and Toda systems, [in:] Geometry and Nonlinearity, J. Cieśliński and D. Wójcik (eds.) pp. 227-236, Polish Scientific Publishers, Warsaw 1998.

  18. A. Doliwa, M. Mañas, L. Martínez Alonso, E. Medina and P.M. Santini, Charged free fermions, vertex operators and transformation theory of conjugate nets, J. Phys. A 32 (1999) 1197-1216, doi: 10.1088/0305-4470/32/7/010.

  19. A. Doliwa, Quadratic reductions of quadrilateral lattices, J. Geom. Phys. 30 (1999) 169-186, doi:10.1016/S0393-0440(98)00053-9.

  20. A. Doliwa, Discrete geometry with ruler and compass, [in:] Symmetries and Integrability of Difference Equations, P. Clarkson and F. Nijhoff (eds.) pp. 122-136, Cambridge University Press, 1999.

  21. A. Doliwa and P.M. Santini, Geometry of discrete curves and lattices and integrable difference equations, [in:] Discrete Integrable Geometry and Physics, A. Bobenko and R. Seiler (eds.), pp.139-154, Clarendon Press, Oxford 1999.

  22. A. Doliwa, P.M. Santini and M. Mañas, Transformations of quadrilateral lattices, J. Math. Phys. 41 (2000) 944-990, doi:10.1063/1.533175.

  23. A. Doliwa, M. Mañas and L. Martínez Alonso, Generating quadrilateral and circular lattices in KP theory, Phys. Lett. A 262 (1999) 330-343, doi: 10.1016/S0375-9601(99)00579-4.

  24. A. Doliwa and P.M. Santini, The symmetric, D-invariant and Egorov reductions of the quadrilateral lattice, J. Geom. Phys. 36 (2000) 60-102, doi: 10.1016/S0393-0440(00)00011-5.

  25. A. Doliwa, Lattice geometry of the Hirota equation, [in:] SIDE III - Symmetries and Integrability of Difference Equations, D. Levi and O. Ragnisco (eds.) pp. 93-100, AMS, Providence 2000.

  26. A. Doliwa and P.M. Santini, Integrable discrete geometry: the quadrilateral lattice, its transformations and reductions, [in:] SIDE III - Symmetries and Integrability of Difference Equations, D. Levi and O. Ragnisco (eds.) pp. 101-119, AMS, Providence 2000.

  27. A. Doliwa, The Ribaucour congruences of spheres within Lie sphere geometry, [in:] Bäcklund and Darboux transformations: the Geometry of Soliton Theory, Halifax 1999, C. Rogers and P. Winternitz (eds.), pp. 159-166, AMS, Providence, 2001.

  28. A. Doliwa, Discrete asymptotic nets and W-congruences in Plücker line geometry, J. Geom. Phys. 39 (2001) 9-29, doi: 10.1016/S0393-0440(00)00070-X.

  29. A. Doliwa, The Darboux-type transformations of integrable lattices, Rep. Math Phys. 48 (2001) 59-66, doi: 10.1016/S0034-4877(01)80064-1.

  30. A. Doliwa, Asymptotic lattices and W-congruences in integrable discrete geometry, J. Nonlin. Math. Phys. 8 (2001) 88-92, Supplement Proceedings of the 13th Workshop NEEDS'99, B. Pelloni, M. Bruschi and O. Ragnisco (eds.) doi: 10.2991/jnmp.2001.8.s.16 .

  31. A. Doliwa, Integrable Multidimensional Discrete Geometry: Quadrilateral Lattices, their Transformations and Reductions, [in:] Integrable Hierarchies and Modern Physical Theories, H. Aratyn and A. S. Sorin (eds.), pp. 355-389, Kluwer, Dordrecht, 2001.

  32. M. Nieszporski, A. Doliwa and P. M. Santini, The integrable discretization of the Bianchi-Ernst system, nlin.SI/0104065 .

  33. A. Doliwa, M. Nieszporski and P. M. Santini, Asymptotic lattices and their integrable reductions I: the Bianchi and the Fubini-Ragazzi lattices, J. Phys. A 34 (2001) 10423-10439, doi: 10.1088/0305-4470/34/48/308.

  34. A. Doliwa, Geometric discretization of the Koenigs nets, J. Math. Phys. 44 (2003) 2234-2249, doi:10.1063/1.1563041.

  35. A. Doliwa, M. Białecki and P. Klimczewski, The Hirota equation over finite fields. Algebro-geometric approach and multisoliton solutions, J. Phys. A 36 (2003) 4827-4839, doi: 10.1088/0305-4470/36/17/309.

  36. M. Białecki and A. Doliwa, The discrete KP and KdV equations over finite fields, Theor. Math. Phys. 137 (2003) 1412-1418.

  37. M. Nieszporski, P. M. Santini and A. Doliwa, Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrödinger operator, Phys. Lett. A 323 (2004) 241-250, doi: 10.1016/j.physleta.2004.02.003.

  38. M. Białecki and A. Doliwa, Algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve, Comm. Math. Phys. 253 (2005) 157-170, doi: 10.1007/s00220-004-1207-3.

  39. A. Doliwa, M. Nieszporski and P. M. Santini, Geometric discretization of the Bianchi system, J. Geom. Phys. 52 (2004) 217-240, doi: 10.1016/j.geomphys.2004.02.010

  40. A. Doliwa, The normal dual congruences and the dual Bianchi lattice, Glasgow Math. J. 47A (2005) 51-63, doi: 10.1017/S0017089505002284.

  41. P. M. Santini, M. Nieszporski and A. Doliwa, Integrable generalization of the Toda law to the square lattice, Phys. Rev. E 70 (2004) 056615, doi: 10.1103/PhysRevE.70.056615 .

  42. A. Doliwa, On τ-function of conjugate nets, J. Nonlin. Math. Phys. 12 (2005) 244-252, Supplement Special Issue in Honour of Francesco Calogero On the Occasion of His 70th Birthday, N. Euler (ed.) doi: 10.2991/jnmp.2005.12.s1.20.

  43. A. Doliwa, P. Grinevich, M. Nieszporski and P. M. Santini, Integrable lattices and their sub-lattices: from the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme, J. Math. Phys. 48 (2007) 013513, doi:10.1063/1.2406056.

  44. A. Doliwa and P. M. Santini, Integrable Systems and Discrete Geometry, [in:] Encyclopedia of Mathematical Physics, J. P. Françoise, G. Naber and T. S. Tsun (eds.) Vol. III, pp. 78-87, Elsevier, 2006, doi: 10.1016/B0-12-512666-2/00178-4.

  45. A. Doliwa, The B-quadrilateral lattice, its transformations and the algebro-geometric construction, J. Geom. Phys.  57 (2007) 1171-1192, doi: 10.1016/j.geomphys.2006.09.010.

  46. A. Doliwa, Generalized isothermic lattices, J. Phys. A: Math. Theor. 40 (2007) 12539-12561, doi: 10.1088/1751-8113/40/42/S03.

  47. A. Doliwa, M. Nieszporski and P. M. Santini, Integrable lattices and their sub-lattices II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices, J. Math. Phys. 48 (2007) 113506, doi:10.1063/1.2803504

  48. P. M. Santini, A. Doliwa and M. Nieszporski, Integrable dynamics of Toda-type on the square and triangular lattice, Phys. Rev. E 77 (2008) 056601, doi: 10.1103/PhysRevE.77.056601.

  49. A. Doliwa, The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction, J. Geom. Phys. 60 (2010) 690-707, doi: 10.1016/j.geomphys.2010.01.005.

  50. A. Doliwa, Geometric algebra and quadrilateral lattices, arXiv:0801.0512

  51. A. Doliwa, The τ-function of the quadrilateral lattice, J. Phys. A: Math. Theor. 42 (2009) 404008, doi: 10.1088/1751-8113/42/40/404008.

  52. A. Doliwa, M. Nieszporski, Darboux transformations for linear operators on two dimensional regular lattices, J. Phys. A: Math. Theor. 42 (2009) 454001, doi: 10.1088/1751-8113/42/45/454001.

  53. A. Doliwa, Desargues maps and the Hirota-Miwa equation, Proc. R. Soc. A 466 (2010) 1177-1200, doi: 10.1098/rspa.2009.0300.

  54. A. Doliwa, The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system, Phys. Lett. A 375 (2011) 1219-1224, doi: 10.1016/j.physleta.2011.01.050.

  55. A. Doliwa, S. M. Sergeev, The pentagon relation and incidence geometry, J. Math. Phys. 55 (2014) 063504 (21pp), doi: 10.1063/1.4882285

  56. A. Doliwa, Hirota equation and the quantum plane, [in:] Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, A. Dzhamay, K. Maruno, V. Pierce (eds.), Contemporary Mathematics, vol. 593, Amer. Math. Soc., Providence, RI, 2013, pp. 205-230, doi: 10.1090/conm/593/11871

  57. A. Doliwa, Non-commutative lattice modified Gel'fand-Dikii systems, J. Phys. A: Math. Theor. 46 (2013) 205202 (14pp), doi:10.1088/1751-8113/46/20/205202 .

  58. A. Doliwa, Desargues maps and their reductions, [in:] Nonlinear and Modern Mathematical Physics, W.X. Ma, D. Kaup (eds.), AIP Conference Proceedings, Vol. 1562, AIP Publishing 2013, pp. 30-42, doi: 10.1063/1.4828680

  59. A. Doliwa, Non-commutative rational Yang-Baxter maps, Lett. Math. Phys. 104 (2014) 299-309, doi:10.1007/s11005-013-0669-7 .

  60. A. Doliwa, R. Lin, Discrete KP equation with self-consistent sources, Phys. Lett. A 378 (2014) 1925-1931, doi:10.1016/j.physleta.2014.04.021 .

  61. A. Doliwa, Non-commutative q-Painlevé VI equation, J. Phys. A: Math. Theor. 47 (2014) 035203, doi:10.1088/1751-8113/47/3/035203 .

  62. A. Doliwa, A. M. Grundland, Minimal surfaces in the soliton surface approach, arXiv:1511.02173

  63. A. Doliwa, Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables, Electron. J Combin. 28 (2021) P2.50, doi: 10.37236/10184

  64. A. Doliwa, J. Kosiorek, Quadrangular sets in projective line and in Moebius space, and geometric interpretation of the non-commutative discrete Schwarzian Kadomtsev-Petviashvili equation, Asymptotic, Algebraic and Geometric Aspects of Integrable Systems, F. Nijhoff, Y. Shi, D. Zhang (eds). Springer Proceedings in Mathematics & Statistics, Vol. 338 Springer 2020, pp. 1-15, doi: 10.1007/978-3-030-57000-2_1

  65. A. Doliwa, Non-commutative double-sided continued fractions, J. Phys. A: Math. Theor. 53 (2020) 364001 (23 pp.) doi: 10.1088/1751-8121/aba29c

  66. A. Doliwa, M. Noumi, The Coxeter relations and KP map for non-commuting symbols, Lett. Math. Phys. 110 (2020) 2743–2762, doi: 10.1007/s11005-020-01317-6

  67. A. Doliwa, R. M. Kashaev, Non-commutative bi-rational maps satisfying Zamolodchikov equation, and Desargues lattices, J. Math. Phys. 61 (2020) 092704 (23pp.) doi: 10.1063/5.0016474

  68. A. Doliwa, R. L. Lin, Z. Wang, Discrete Darboux system with self-consistent sources and its symmetric reduction, J. Phys. A: Math. Theor. 54 (2021) 054001 (22 pp.) doi: 10.1088/1751-8121/abd814

  69. A. Doliwa, A. Siemaszko, Integrability and geometry of the Wynn recurrence, Numer. Algorithms 92 (2023) 571-596, doi: 10.1007/s11075-022-01344-5

  70. A. Doliwa, A. Siemaszko, Hermite-Padé approximation and integrability, J. Approx. Theory 292 (2023) 105910 (23 pp.) doi: 10.1016/j.jat.2023.105910

  71. A. Doliwa, Non-commutative Hermite-Padé approximation and integrability, Lett. Math. Phys. 112 (2022) 68 (17 pp.) doi: 10.1007/s11005-022-01560-z

  72. A. Doliwa, Non-autonomous multidimensional Toda system and multiple interpolation problem, J. Phys. A: Math. Theor. 55 (2022) 505202 (17 pp.) doi: 10.1088/1751-8121/acad4d

  73. A. Doliwa, A. Siemaszko, Spectral quantization of discrete random walks on half-line, and orthogonal polynomials on the unit circle, arXiv:2306.12265

  74. A. Doliwa, Bäcklund transformations as integrable discretization. The geometric approach, Open Commun. in Nonlin. Math. Phys., Special Issue in Memory of Decio Levi (2024) 12215 (28 pp.) doi: 10.46298/ocnmp.12215

  75. A. Doliwa, Hermite-Padé approximation, multiple orthogonal polynomials, and multidimensional Toda equations, arXiv:2310.15116

  76. A. Doliwa, Determinantal approach to multiple orthogonal polynomials, and the corresponding integrable equations, Stud. Appl. Math. doi: 10.1111/sapm.12726

    A.D. 16.06.2024