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.
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.
A. Doliwa and A. Sym, Minimal surfaces in S2m and Toda Systems, Warsaw University preprint No. IFT 11/92.
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.
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.
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.
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.
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.
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.
A. Doliwa, Harmonic maps and Toda systems, J. Math. Phys. 38 (1997) 1685-1691, doi:10.1063/1.531822.
A. Doliwa, Holomorphic curves and Toda systems, Lett. Math. Phys. 39 (1997) 21-32, doi: 10.1007/s11005-997-1032-7.
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.
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.
A. Doliwa, Geometric discretisation of the Toda system, Phys. Lett. A 234 (1997) 187-192, doi: 10.1016/S0375-9601(97)00477-5.
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.
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.
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.
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.
A. Doliwa, Quadratic reductions of quadrilateral lattices, J. Geom. Phys. 30 (1999) 169-186, doi:10.1016/S0393-0440(98)00053-9.
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.
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.
A. Doliwa, P.M. Santini and M. Mañas, Transformations of quadrilateral lattices, J. Math. Phys. 41 (2000) 944-990, doi:10.1063/1.533175.
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.
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.
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.
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.
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.
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.
A. Doliwa, The Darboux-type transformations of integrable lattices, Rep. Math Phys. 48 (2001) 59-66, doi: 10.1016/S0034-4877(01)80064-1.
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 .
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.
M. Nieszporski, A. Doliwa and P. M. Santini, The integrable discretization of the Bianchi-Ernst system, nlin.SI/0104065 .
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.
A. Doliwa, Geometric discretization of the Koenigs nets, J. Math. Phys. 44 (2003) 2234-2249, doi:10.1063/1.1563041.
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.
M. Białecki and A. Doliwa, The discrete KP and KdV equations over finite fields, Theor. Math. Phys. 137 (2003) 1412-1418.
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.
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.
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
A. Doliwa, The normal dual congruences and the dual Bianchi lattice, Glasgow Math. J. 47A (2005) 51-63, doi: 10.1017/S0017089505002284.
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 .
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.
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.
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.
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.
A. Doliwa, Generalized isothermic lattices, J. Phys. A: Math. Theor. 40 (2007) 12539-12561, doi: 10.1088/1751-8113/40/42/S03.
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
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.
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.
A. Doliwa, Geometric algebra and quadrilateral lattices, arXiv:0801.0512
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.
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.
A. Doliwa, Desargues maps and the Hirota-Miwa equation, Proc. R. Soc. A 466 (2010) 1177-1200, doi: 10.1098/rspa.2009.0300.
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.
A. Doliwa, S. M. Sergeev, The pentagon relation and incidence geometry, J. Math. Phys. 55 (2014) 063504 (21pp), doi: 10.1063/1.4882285
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
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 .
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
A. Doliwa, Non-commutative rational Yang-Baxter maps, Lett. Math. Phys. 104 (2014) 299-309, doi:10.1007/s11005-013-0669-7 .
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 .
A. Doliwa, Non-commutative q-Painlevé VI equation, J. Phys. A: Math. Theor. 47 (2014) 035203, doi:10.1088/1751-8113/47/3/035203 .
A. Doliwa, A. M. Grundland, Minimal surfaces in the soliton surface approach, arXiv:1511.02173
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
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
A. Doliwa, Non-commutative double-sided continued fractions, J. Phys. A: Math. Theor. 53 (2020) 364001 (23 pp.) doi: 10.1088/1751-8121/aba29c
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
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
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
A. Doliwa, A. Siemaszko, Integrability and geometry of the Wynn recurrence, Numer. Algorithms 92 (2023) 571-596, doi: 10.1007/s11075-022-01344-5
A. Doliwa, A. Siemaszko, Hermite-Padé approximation and integrability, J. Approx. Theory 292 (2023) 105910 (23 pp.) doi: 10.1016/j.jat.2023.105910
A. Doliwa, Non-commutative Hermite-Padé approximation and integrability, Lett. Math. Phys. 112 (2022) 68 (17 pp.) doi: 10.1007/s11005-022-01560-z
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
A. Doliwa, A. Siemaszko, Spectral quantization of discrete random walks on half-line, and orthogonal polynomials on the unit circle, arXiv:2306.12265
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
A. Doliwa, Hermite-Padé approximation, multiple orthogonal polynomials, and multidimensional Toda equations, arXiv:2310.15116
A. Doliwa, Determinantal approach to multiple orthogonal polynomials, and the corresponding integrable equations, Stud. Appl. Math. 153 (2024) e12726 (26 pp.) doi: 10.1111/sapm.12726
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