##
Folkert Müller-Hoissen:

Scientific Publications

Scientific Publications

- "On the structure of set-theoretic polygon equations"

arXiv:2305.17974 [math-ph] . - "A vectorial binary Darboux transformation for the
first member of the negative part of the AKNS
hierarchy"

J. Phys. A: Math. Theor.**56**(2023) 125701, preprint arXiv:2202.04512 [nlin.PS]. - "Obituary: Aristophanes Dimakis"

arXiv:2108.05695 [physics.hist-ph]. - "Tropical limit of matrix solitons and entwining Yang-Baxter maps"

with A. Dimakis, Lett. Math. Phys.**110**(2020) 3015-3051, preprint arXiv:2001.09688 [nlin.SI]. - "Matrix Boussinesq solitons and their tropical limit"

with A. Dimakis and X.-M. Chen,*Physica Scripta***94**(2019) 035206, preprint arXiv:1805.09711 [nlin.SI]. - "Differential Calculi on Associative Algebras and Integrable Systems"

with A. Dimakis, Chapter 16 in*Algebraic Structures and Applications*, eds. S. Silvestrov, A. Malyarenko and M. Rančić, Springer Proceedings in Mathematics & Statistics**317**, Springer 2020, 385-410, preprint arXiv:1801.00589. - "Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants"

with Xiao-Min Chen and Xing-Biao Hu,*Nonlinearity***31**(2018) 4393-4422, preprint arXiv:1712.01730. - "Matrix KP: tropical limit, Yang-Baxter and pentagon maps"

with A. Dimakis,*Theor. Math. Phys.***196**(2018) 1164-1173, preprint arXiv:1709.09848. - "Matrix KP: tropical limit and Yang-Baxter maps"

with A. Dimakis,*Lett. Math. Phys.***109**(2019) 799-827, preprint arXiv:1708.05694. - "NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks"

with O. Chvartatskyi, J. Phys. A: Math. Theor.**50**(2017) 155204 .

Preprint version: arXiv:1609.03391.

**Erratum:**In the caption of Figure 5, "t → t_{0}" should read "t → t-t_{0}". - "Generalized Volterra lattices: binary Darboux transformations and self-consistent sources"

with O. Chvartatskyi and K. Toda, Journal of Geometry and Physics**113**(2017) 226-238.

Preprint version: arXiv:1606.03744. - "Self-consistent sources for integrable equations via deformations of binary Darboux Transformations"

with O. Chvartatskyi and A. Dimakis, Lett. Math. Phys.**106**(2016) 1139-1179.

Preprint version: arXiv:1510.05166.

**Erratum:**Section 4, page 1150: the factor in front of the cubic nonlinearities in (4.5) should be 1/4 (instead of 3/2). There are also typos in Example 4.2. Section 7, page 1158: in the first equation (expression for df) the minus sign has to be deleted. - "Higher Bruhat and Tamari orders and their realizations"

with A. Dimakis, J. Generalized Lie Theory Appl.**9**(2015) e103.

- "Simplex and polygon equations"

with A. Dimakis, SIGMA**11**(2015) 042.

Preprint version: arXiv:1409.7855. - " "Riemann equations" in bidifferential calculus"

with O. Chvartatskyi and N. Stoilov, J. Math. Phys.**56**(2015) 103512.

Preprint version: arXiv:1409.1154. - "KdV soliton interactions: a tropical view"

with A. Dimakis, J. Phys. Conf. Series 482 (2014) 012010 , arXiv:1308.1545.

Erratum: In (3.1) "log" is missing before the summation symbol. - "Binary Darboux transformations in bidifferential calculus and integrable reductions
of vacuum Einstein equations"

with A. Dimakis, SIGMA 9 (2013) 009 (31 pages). - "KP solitons, higher Bruhat and Tamari orders"

with A. Dimakis, in:*Associahedra, Tamari Lattices and Related Structures*, Tamari Memorial Festschrift, eds. F. Müller-Hoissen, J. Pallo and J. Stasheff, Progress in Mathematics**299**(Birkhäuser, Basel, 2012) 391-423.

Preprint version: arXiv:1110.3507 [math.CO]. - "Dov Tamari (formerly Bernhard Teitler)"

with H.-O. Walther, in:*Associahedra, Tamari Lattices and Related Structures*, Tamari Memorial Festschrift, eds. F. Müller-Hoissen, J. Pallo and J. Stasheff, Progress in Mathematics**299**(Birkhäuser, Basel, 2012) 1-40. - "The non-autonomous chiral model and the Ernst equation of General Relativity in the bidifferential calculus framework"

with A. Dimakis and N. Kanning, SIGMA 7 (2011) 118. - "Bidifferential calculus, matrix SIT and sine-Gordon equations"

with A. Dimakis and N. Kanning, Acta Polytechnica 51 (2011) 33-37.

Preprint version: arXiv:1011.1737 [nlin]. - "KP line solitons and Tamari lattices"

with A. Dimakis, arXiv:1009.1886 [math-ph], J. Phys. A: Math. Theor. 44 (2011) 025203. - "Bidifferential calculus approach to AKNS hierarchies and their solutions"

with A. Dimakis, arXiv:1004.1627 [nlin], SIGMA 6 (2010) 055. - "Solutions of matrix NLS systems and their discretizations: A unified treatment"

with A. Dimakis, Inverse Problems 26 (2010) 095007, arXiv:1001.0133 [nlin]. - "Quasi-symmetric functions and the KP hierarchy"

with A. Dimakis, arXiv:0901.2562 [math-ph], J. Pure and Applied Algebra 214 (2010) 449-460. - "Multicomponent Burgers and KP hierarchies, and solutions from a matrix
linear system"

with A. Dimakis, arXiv:0811.0110 [nlin.SI], SIGMA 5 (2009) 002. - "BKP and CKP revisited: The odd KP system"

with A. Dimakis, arXiv:0810.0757 [nlin.SI], Inverse Problems 25 (2009) 045001. - "Bidifferential graded algebras and integrable systems"

with A. Dimakis, arXiv:0805.4553 [nlin.SI], Discrete and Continuous Dynamical Systems (DCDS) Supplements 2009, 208-219 (Proceedings AIMS Conference, Arlington 2008). - "Weakly non-associative algebras and the Kadomtsev-Petviashvili hierarchy"

with A. Dimakis, Glasgow Math. J. 51A (2009) 49-57. - "From the Kadomtsev-Petviashvili equation halfway to Ward's chiral model"

with A. Dimakis, arXiv:0712.3689 [nlin.SI], J. Gen. Lie Theory Appl. 2 (2008) 141-146. - "Noncommutative Geometries and Gravity"

arXiv:0710.4418 [gr-qc], AIP Conference Proceedings 977 (2008) 12-29 (3rd Mexican Meeting on Mathematical and Experimental Physics, Symposium on Gravitation and Cosmology, Mexico City, 10-14 September 2007). - "Dispersionless limit of the noncommutative potential KP hierarchy
and solutions of the pseudodual chiral model in 2+1 dimensions"

with A. Dimakis, arXiv:0706.1373 [nlin.SI], J. Phys. A: Math. Theor. 41 (2008) 265205. - "A new approach to deformation equations of noncommutative KP
hierarchies"

with A. Dimakis, math-ph/0703067, J. Phys. A: Math. Theor. 40 (2007) 7573-7596. - "With a Cole-Hopf transformation to solutions of the noncommutative KP
hierarchy in terms of Wronski matrices"

with A. Dimakis, nlin.SI/0701052, J. Phys. A: Math. Theor. 40 (2007) F321-F329.

Erratum: In Proposition 3, Φ should be φ. The signs have to be opposite in the last two parts of equation (29). - "Weakly nonassociative algebras, Riccati and KP hierarchies"

with A. Dimakis, nlin.SI/0701010, in "Generalized Lie Theory in Mathematics, Physics and Beyond", eds. S. Silvestrov, E. Paal, V. Abramov and A. Stolin, (Springer, 2008) (Proceedings of the workshop "Algebra, Geometry, and Mathematical Physics", Lund, October 2006), 9-27. - "Burgers and KP hierarchies: A functional representation approach"

with A. Dimakis, nlin.SI/0610045, Theor. Math. Phys. 152 (2007) 933-947. (Note: The publishers incorrectly shifted part of footnote 3 to the end of proposition 1. The download offered here yields a corrected version.) - "From nonassociativity to solutions of the KP hierarchy"

with A. Dimakis, nlin.PS/0608017, Czech. J. Phys. 56 (2006) 1123-1130. - "From AKNS to derivative NLS hierarchies via deformations of
associative products"

with A. Dimakis, nlin.SI/0603048, J. Phys. A: Math. Gen. 39 (2006) 14015-14033. - "Functional representations of integrable hierarchies"

with A. Dimakis, nlin.SI/0603018, J. Phys. A: Math. Gen. 39 (2006) 9169-9186. - "Nonassociativity and integrable hierarchies"

with A. Dimakis, nlin.SI/0601001. - "Algebraic identities associated with KP and AKNS hierarchies"

with A. Dimakis, math-ph/0507024, Czech. J. Phys. 55 (2005) 1385-1390. - "An algebraic scheme associated with the noncommutative KP
hierarchy and some of its extensions"

with A. Dimakis, nlin.SI/0501003, J. Phys. A: Math. Gen. 38 (2005) 5453-5505. - "Extension of Moyal-deformed hierarchies of soliton equations"

with A. Dimakis, nlin.SI/0408023,

published in XI International Conference Symmetry Methods in Physics,

eds C. Burdik, O. Navratil and S. Posta, Joint Institute for Nuclear Research, Dubna, 2004. - "Differential calculi on quantum spaces determined by
automorphisms"

with A. Dimakis, math.QA/0407273, Czech. J. Phys. 54 (2004) 1235-1242. - "Explorations of the extended ncKP hierarchy"

with A. Dimakis, hep-th/0406112, J. Phys. A: Math. Gen. 37 (2004) 10899-10930. - "Extension of noncommutative soliton hierarchies"

with A. Dimakis, hep-th/0401142, J. Phys. A: Math. Gen. 37 (2004) 4069-4084. - "Automorphisms of associative algebras and noncommutative
geometry"

with A. Dimakis, math-ph/0306058, J. Phys. A: Math. Gen. 37 (2004) 2307-2330. - Five contributions, jointly with A. Dimakis, to: Concise Encyclopedia of Supersymmetry, eds S. Duplij, W. Siegel and J. Bagger (Kluwer, Dordrecht, 2004).
- "Riemannian geometry of bicovariant group lattices"

with A. Dimakis, math-ph/0212054, J. Math. Phys. 44 (2003) 4220-4259

Additional material. - "Differential geometry of group lattices"

with A. Dimakis, math-ph/0207014, J. Math. Phys. 44 (2003) 1781-1821. - "On generalized Lotka-Volterra lattices"

with A. Dimakis, nlin.SI/0207010, Czech. J. Phys. 52 (2002) 1187-1193. - "Noncommutative NLS equation"

with A. Dimakis, Czech. J. Phys. 51 (2001) 1285-1290. - "Bicomplexes and Bäcklund transformations"

with A. Dimakis, nlin.SI/0104071, J. Phys. A: Math. Gen. 34 (2001) 9163-9194. - "Bicomplex formulation and Moyal deformation of
(2+1)-dimensional Fordy-Kulish systems"

with A. Dimakis, nlin.SI/0008016, J. Phys. A: Math. Gen. 34 (2001) 2571-2581. - "Moyal deformation, Seiberg-Witten map, and integrable models"

with A. Dimakis, hep-th/0007160, Lett. Math. Phys. 54 (2000) 123-135. - "The Korteweg-de-Vries equation on a noncommutative space-time"

with A. Dimakis, hep-th/0007074, Phys. Lett. A 278 (2000) 139-145. - "A noncommutative version of the nonlinear Schrödinger equation"

with A. Dimakis, hep-th/0007015. - "Bicomplexes and integrable models"

with A. Dimakis, nlin.SI/0006029, J. Phys. A: Math. Gen. 33 (2000) 6579-6591. - "Bicomplexes, integrable models, and noncommutative geometry"

with A. Dimakis, hep-th/0006005, Int. J. Mod. Phys. B14 (2000) 2455-2460. - "Bicomplexes and finite Toda lattices"

with A. Dimakis, solv-int/9911006, in: Quantum Theory and Symmetries, eds. H.-D. Doebner, V.K. Dobrev, J.-D. Hennig and W. Lücke (World Scientific, 2000) 545-549. - "Bi-differential calculus and the KdV equation"

with A. Dimakis, math-ph/9908016, Rep. Math. Phys. 46 (2000) 203-210. - "Bi-differential calculi and integrable models"

with A. Dimakis, math-ph/9908015, J. Phys. A: Math. Gen. 33 (2000) 957-974. - "Pseudo-Riemannian metrics in models based on noncommutative geometry"

with A. Dimakis, gr-qc/9908022, Czech. J. Phys. 50 (2000) 45-52. - "Noncommutative geometry and a class of completely integrable
models"

with A. Dimakis, math-ph/9809023, Czech. J. Phys. 48 (1998) 1319-1324. - "Discrete Riemannian geometry"

with A. Dimakis, gr-qc/9808023, J. Math. Phys. 40 (1999) 1518-1548. - "Deformations of classical geometries and integrable systems"

with A. Dimakis, preprint GOET-TP 100/97, physics/9712002.

Talk presented at the workshop "Quantum Groups, Deformations and Contractions", Bogazici University, Istanbul, September 1997. Submitted to the proceedings which apparently never appeared in print. - "Some aspects of noncommutative geometry and physics"

with A. Dimakis, physics/9712004, in: Novelties in String Theory, eds. L. Brink and R. Marnelius (World Scientific, 1999) 327-347. - "Connes' distance function on one-dimensional lattices"

with A. Dimakis, q-alg/9707016, Int. J. Theor. Phys. 37 (1998) 907-913. - "Introduction to Noncommutative Geometry of Commutative Algebras
and Applications in Physics"

in Recent Developments in Gravitation and Mathematical Physics, Proceedings of the Second Mexican School on Gravitation and Mathematical Physics, eds. A. Garcia, C. Lämmerzahl, A. Macias, T. Matos, and D. Nunez, Science Network Publishing 1998, ISBN 3-9805735-0-8

postscript file - "A generalization of sigma-models and complete integrability"

with A. Dimakis, in GROUP21, Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, Vol. 2, Eds: H.-D. Doebner, W. Scherer and C. Schulte, World Scientific 1997, pp. 602-606. - "Soliton equations and the zero curvature condition in
noncommutative geometry"

with A. Dimakis, hep-th/9608009, J. Phys. A 29 (1996) 7279-7286. - "Noncommutative geometry and integrable models"

with A. Dimakis, Lett. Math. Phys. 39 (1997) 69-79. - "Umbral calculus, discretization, and quantum mechanics on
a lattice"

with A. Dimakis and T. Striker, quant-ph/9509014, J. Phys. A 29 (1996) 6861-6876. - "Integrable discretizations of chiral models via deformation
of the differential calculus"

with A. Dimakis, hep-th/9512007, J. Phys. A: Math. Gen. 29 (1996) 5007-5018. - "Noncommutative geometry of finite groups"

with K. Bresser, A. Dimakis and A. Sitarz, q-alg/9509004, J. Phys. A 29 (1996) 2705-2735. - "Discrete differential manifolds and physics"

with A. Dimakis, in: Nonlinear, Deformed and Irreversible Quantum Systems, eds. H.-D. Doebner, V.K. Dobrev and P. Nattermann (World Scientific,1995) pp. 469-474. - "Differential calculi on commutative algebras"

with H. Baehr and A. Dimakis, preprint MPI-PhT/94-83, hep-th/9412069, J. Phys. A 28 (1995) 3197-3222. - "Discrete differential manifolds and dynamics on networks"

with A. Dimakis und F. Vanderseypen, hep-th/9408114, J. Math. Phys. 36 (1995) 3771-3791. - "Physical aspects of differential calculi on commutative
algebras"

in: Quantum Groups, Formalism and Applications, XXX Karpacz Winter School of Theoretical Physics, eds. J. Lukierski, Z. Popowicz and J. Sobczyk (Polish Scientific Publishers, Warszawa, 1995) pp. 267-289. - "Discrete differential calculus: Graphs, topologies, and gauge
theory"

with A. Dimakis hep-th/9404112, J. Math. Phys. 35 (1994) 6703-6735. - "Differential calculus and discrete structures"

with A. Dimakis, hep-th/9401150, in: Generalized Symmetries in Physics, eds. H.-D. Doebner, V.K. Dobrev and A.G. Ushveridze (World Scientific, Singapore, 1994), pp. 213-218. - "Differential calculi on quantum (sub-) groups and
their classical limit"

in: Generalized Symmetries in Physics, eds. H.-D. Doebner, V.K. Dobrev and A.G. Ushveridze (World Scientific, Singapore, 1994), pp. 196-207. - "Noncommutative differential calculus: quantum groups,
stochastic processes, and the antibracket"

with A. Dimakis, hep-th/9401151, in: Proceedings of the XXII International Conference on Differential Geometric Methods in Theoretical Physics, Ixtapa, Mexico, Sept. 1993, published in: Advances in Applied Clifford Algebras (Proc. Suppl.) 4(S1) (1994) 113-124, arXiv:hep-th/9401151. - "Differential forms and gauge theory on discrete sets
and lattices"

with A. Dimakis, in the proceedings of the workshop `Symmetry Methods in Physics' in memory of Ya. A. Smorodinsky, Dubna, July 1993, Vol. 2, 351-357. - "Differential calculus and gauge theory on finite sets"

with A. Dimakis hep-th/9401149, J. Phys. A: Math. Gen. 27 (1994) 3159-3178. - "Noncommutative differential calculus, quantum groups, and
computer algebra"

in: Proceedings SC93, International IMACS Symposium on Symbolic Computation, Lille 1993, eds. G. Jacob, N.E. Oussous and S. Steinberg, pp. 97-102. - "Stochastic differential calculus, the Moyal *-product,
and noncommutative geometry"

with A. Dimakis Lett. Math. Phys. 28 (1993) 123-137. - "Bicovariant differential calculi on GLp,q(2) and
quantum subgroups"

with C. Reuten, J. Phys. A: Math. Gen. 26 (1993) 2955-2975. - "Some applications of noncommutative differential calculus
in physics"

habilitation thesis, Göttingen 1992. - "Noncommutative differential calculus and lattice gauge
theory"

with A.Dimakis and T.Striker, J. Phys. A: Math. Gen. 26 (1993) 1927-1949. - "From continuum to lattice theory via deformation of the
differential calculus"

with A.Dimakis and T.Striker, Phys. Lett. B 300 (1993) 141-144. - "Quantum mechanics on a lattice and q-deformations"

with A.Dimakis Phys. Lett. B 295 (1992) 242-248 . - "A noncommutative differential calculus and its relation to
gauge theory and gravitation"

with A.Dimakis, in Proceedings of the XXI International Conference on Differential Geometric Methods in Theoretical Physics, Tianjin (China), June 1992, Int. J. Mod. Phys. A (Proc. Suppl.) 3A (1993) 474-477. - "Noncommutative symplectic geometry and quantum mechanics"

with A.Dimakis, in Proceedings of the XXI International Conference on Differential Geometric Methods in Theoretical Physics, Tianjin (China), June 1992, Int. J. Mod. Phys. A (Proc. Suppl.) 3A (1993) 214-217. - "Noncommutative differential calculus, gauge theory and
gravitation"

with A.Dimakis preprint GOET-TP 33/92. - "Quantum mechanics as noncommutative symplectic geometry"

with A.Dimakis J. Phys. A: Math. Gen. 25 (1992) 5625-5648. - "Differential calculi on the quantum group GLp,q(2)"

J. Phys. A: Math. Gen. 25 (1992) 1703-1734. - "Higher derivative versus second order field equations"

Annalen der Physik (Leipzig) 48 (1991) 543-557. - "Clifform calculus with applications to classical field theories"

with A.Dimakis Class. Quantum Grav. 8 (1991) 2093-2132. - "From Chern-Simons to Gauss-Bonnet"

Nucl. Phys. B 346 (1990) 235-252. - "Gauss-Bonnet actions and their dimensionally reduced
descendants"

in Fisica de Particulas e Campos, X Encontro Nacional 1989 (Sociedade Brasileira de Fisica) pp. 116-124. - "Gravity actions, boundary terms and second order field
equations"

Nucl. Phys. B 337 (1990) 709-736. - "Spinor fields and the positive energy theorem"

with A.Dimakis Class. Quantum Grav. 7 (1990) 283-295. - "On a gauge condition for orthonormal three frames"

with A.Dimakis Phys. Lett. A 142 (1989) 73-74. - "Non-minimal coupling from higher dimensions and
four-dimensional black holes"

in Proc. of the Fifth Marcel Grossmann Meeting on General Relativity, eds. D.Blair, M.Buckingham and R.Ruffini (World Scientific, Singapore, 1989) pp. 625-628. - "Spherically symmetric solutions of the non-minimally coupled
Einstein-Maxwell equations"

with R.Sippel, Class. Quantum Grav. 5 (1988) 1473-1488. - "Modification of Einstein-Yang-Mills theory from dimensional
reduction of the Gauss-Bonnet action"

Class. Quantum Grav. 5 (1988) L35-L40. - "Non-minimal coupling from dimensional reduction of the
Gauss-Bonnet action"

Phys. Lett. B 201 (1988) 325-327. - "Coset spaces and ten-dimensional unified theories"

with R. Stückl, Class. Quantum Grav. 5 (1988) 27-54. - "Spontaneous compactification to non-symmetric coset spaces in
Einstein-Yang-Mills theory"

Class. Quantum Grav. 4 (1987) L143-L148. - "Note on generalized Kaluza-Klein field equations"

Europhysics Letters 3 (1987) 1075-1078 . - "Compactifications with SU(3)xSU(2)xU(1) symmetry
in d=11 Kaluza-Klein theory"

Class. Quantum Grav. 3 (1986) L133-L140. - "Dimensionally continued Euler forms: Kaluza-Klein cosmology and
dimensional reduction"

Class. Quantum Grav. 3 (1986) 665-677. - "Spontaneous compactification with quadratic and cubic curvature
terms"

Phys. Lett. B 163 (1985) 106-110. - "On the tetrad theory of gravity"

with J.Nitsch, Gen. Rel. Grav. 17 (1985) 747-760. - "Solutions of the Einstein-Cartan-Dirac equations with vanishing
energy-momentum tensor"

with A.Dimakis J. Math. Phys. 26 (1985) 1040-1048.

Additional material. - "Spatially homogeneous and isotropic spaces in theories of
gravitation with torsion"

with H.Goenner, Class. Quantum Grav. 1 (1984) 651-672. - "A gauge theoretical approach to space-time structures"

Ann. Inst. Henri Poincare 40 (1984) 21-34 . - "Untersuchungen einer Klasse von Gravitationseichtheorien" (Explorations of a class of gravitational gauge theories), doctoral thesis, Göttingen 1983. (Copies are still available, please contact me.)
- "The cosmological principle and a generalization of Newton's
theory of gravity"

Gen. Rel. Grav. 15 (1983) 1051-1066. - "Teleparallelism - an alternative theory of gravity ?"

with J.Nitsch, in 10th International Conference on General Relativity and Gravitation, Padova (Italy) 1983, Contributed Papers, eds. B.Bertotti et al., pp. 594-596. - "Ghost Dirac fields in theories with torsion"

with A.Dimakis, in 10th International Conference on General Relativity and Gravitation, Padova (Italy) 1983, Contributed Papers, eds. B.Bertotti et al., pp. 505-506. - "Teleparallelism - a viable theory of gravity ?"

with J.Nitsch, Phys. Rev. D 28 (1983) 718-728. - "Friedmann cosmology with torsion"

Phys. Lett. A 92 (1982) 433-434. - "Massive ghost Dirac fields in Einstein-Cartan theory"

with A.Dimakis Phys. Lett. A 92 (1982) 431-432. - "Determinism in space-time"

Int. J. Theor. Phys. 20 (1981) 443-450. - "Raum-Zeit-Ränder" (Space-time boundaries), diploma thesis, Göttingen 1979.