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LIST OF PUBLICATIONS:

Books

1. Steeb W-H and Euler N, Nonlinear Field Equations and Painlev'e Test, World Scientific Publishing, Singapore/New Jersey/Hong Kong, 1988.

2. Euler N and Steeb W-H, Continuous Symmetries, Lie Algebras and Differential Equations, B.I Wissenschaftsverlag, Mannheim/Wien/Zürich, 1992.

3. Euler N, A First Course in Ordinary Differential Equations, E-book at Bookboon.com: London, UK, ISBN: 978-87-403-1045-0, 1st edition (232 pages). July 2015. Free Access

4. Euler M and Euler N, Problems, Theory and Solutions in Linear Algebra, Part 1: Euclidean Space , E-book at Bookboon.com: London, UK, ISBN: 978-87-403-1134-1, 1st edition (169 pages). October 2015; 2nd edition (235 pages) June 2016. Free Access

5. Euler N (translated by Cristina Sardon Munoz) Ecuaciones diferenciales ordinarias: Introduccion a las ecuaciones lineales , E-book at Bookboon.com: London, UK, ISBN: 978-87-403-1213-3, 1st edition (233 pages). January 2016. Free Access

6. Euler N (translated by Ann-Kathrin Kolb) Gewöhnliche Differentialgleichungen. Eine Einführung , E-book at Bookboon.com: London, UK, ISBN:, 978-87-403-1290-4, 1st edition (237 pages). April 2016. Free Access

7. Euler M and Euler N (translated by Cristina Sardon Munoz) Problemas, Teoria y Soluciones en Algebra Lineal: Parte 1 Espacio Euclideo E-book at Bookboon.com: London, UK, ISBN: 978-87-403-1415-1, 1st edition (232 pages). August 2016. Free Access

8. Euler M and Euler N (translated by Ann-Kathrin Kolb) Afgaben, Theorie und Lösungen zur Linearen Algebra. Teil 1: Der Euklidische Raum E-book at Bookboon.com: London, UK, ISBN: 978-87-403-1568-4, 1st edition (241 pages). January 2017. Free Access

9. Euler M and Euler N (translated by Benoit Mahault) Théorie et Problémes Résolus d'Algèbre Linéaire. Volume 1: Espaces Euclidiens E-book at Bookboon.com: London, UK, ISBN: 978-87-403-1867-8, 1st edition (214 pages). August 2017. Free Access

10. Euler N (ed), "Nonlinear Systems and Their Remarkable Mathematical Structures" (Vol. 1) , Currently in press at CRC Press (Boca Raton, FL, USA), 2018. View the Contents, Preface and list of Authors.

Conference Proceedings and Special Issues:

1. Euler N (Editor) Special Issue in Honour of Francesco Calogero on the Occasion of His 70th Birthday, Journal of Nonlinear Mathematical Physics, Supplement 1 to Volume 12, 2005, ISBN: 91-974824-3-9, Taylor and Francis.

2. Basarab-Horwath P, Euler M, Euler N and Leach PGL (Editors) Advances in the Analysis of Differential Equations , Journal of Nonlinear Mathematical Physics, Supplement to Volume 16, 2009, World Scientific.

3. Euler N and Ibragimov N H (Editors) Proceedings of the 14th Conference on Modern Group Analysis, Journal of Nonlinear Mathematical Physics, Supplement 1 to Volume 18, 2011, World Scientific.

Research Papers

1. Steeb W-H and Euler N, Painlev'e Test of the McKean and Carleman Models Lett. Math. Phys., 13, 234-236, 1987

2. Steeb W-H and Euler N, Lie and Lie Bäcklund Vector Fields and Painlev'e Test for a Class of Scale Invariant Partial Differential Equations of First Order Prog. Theor. Phys. 78, 214-223, 1987.

3. Euler N, Leach P G L, Mahomed F M and Steeb W-H, Symmetry Vector Fields and Similarity Solutions of a Nonlinear Field Equation Describing the Relaxation to a Maxwell Distribution, Int. J. Theor. Phys. 27, 717-723, 1988.

4. Steeb W-H and Euler N, A Note on Nambu Mechanics and Painlev'e Test, Prog. Theor. Phys. 80, 607-610, 1988

5. Euler N and Steeb W-H, Painlev'e Test and Discrete Boltzmann Equations, Aust. J. Phys.42, 1-10, 1989.

6. Euler N and Steeb W-H and Cyrus K, On exact solutions for damped anharmonic oscillators, J. Phys. A: Math. Gen. 22, L195-L199, 1989.

7. Euler N and Steeb W-H, Lie-Symmetry Vector Fields for Linear and Nonlinear Wave Equations, Int. J. Theor. Phys. 28, 1397-1403, 1989.

8. Euler N and Steeb W-H, Polynomial Field Theories and Nonintegrability, Phys. Scripta 41, 289-291, 1990.

9. Duarte L G S, Euler N, Moreira I C and Steeb W-H, Invertible point transformations, Painlev'e analysis and anharmonic oscillators, J. Phys. A: Math. Gen. 23, 1457-1463, 1990.

10. Steeb W-H and N Euler, Inviscid Burgers Equation, Painlev'e Analysis and a Bäcklund Transformation, Z. Naturforschung A, 45A, 929-930, 1990.

11. Steeb W-H and Euler N, Nonlinear Dynamical Systems, First Integrals, Bose Operators and Lie Algebras, Found. Phys. Lett. 3, 367-374, 1990.

12. Steeb W-H, S.J.M Brits and Euler N, Painlev'e Test and Energy Level Motion, Int. J. Theor. Phys. 29, 637-642, 1990.

13. Steeb W-H and Euler N, A Note on Nambu Mechanics Nuovo Cimento B, 263-272, 1991.

14. Steeb W-H, Euler N and Mulser P, On a Hierarchy of Nonlinear Dynamical Systems and Painleve Test, Found. of Phys. 4, 465-469, 1991.

15. Duarte L G S, Moreira N, Euler N and Steeb W-H, Invertible Point Transformations, Lie Symmetries and the Painlev'e Test for the Equation  ..., Physica Scripta 43, 449-451, 1991.

16. Steeb W-H, Euler N and Mulser P, Semiclassical Jaynes-Cummings Model, Painlev'e Test and Exact Solutions, J. Math. Phys. 32, 3405-3406, 1991.

17. Euler N, Steeb W-H and Mulser P, Lie Bäcklund Vector Fields and Similarity Solutions, J. Phys. Soc. Jpn 60, 1132-1133, 1991.

18. Euler N, Steeb W-H, Duarte L G S and Moreira I C, Invertible Point Transformation, Painlev'e Test and the Second Painlev'e Transcendent, Int. J. Theor. Phys. 30, 1267-1271, 1991.

19. Euler N, Steeb W-H and Mulser P Symmetries of a Nonlinear Equation in Plasma Physics, J. Phys. A:Math. Gen. 24, L785-L787, 1991.

20. Steeb W-H, Euler N and Mulser P, A note on Integrability and Chaos of Reduced Self-dual Yang-Mills Equations and Yang-Mills Equations, Nuovo Cimento 106B, 1059, 1991.

21. Steeb W-H and Euler N, Nonlinear Evolution Equation and Painlev'e Test, Int. J. Mod. Phys. 7, 1669-1683, 1992.

22. Steeb W-H and Euler N, Parametrically Driven Pendulum and Exact Solutions, Int. J. of Theor. Phys. 31, 1527-1530, 1992.

23. Hereman W, Steeb W-H and Euler N, Comment on `Towards the conservation laws and Lie symmetries for the Khokhlov-Zabolotskaya equation in three dimensions', J. Phys. A: Math. Gen. 25, 2417-2418, 1992.

24. Euler N, Shul'ga M W and Steeb W-H, Approximate symmetries and approximate solutions for a multidimensional Landau-Ginzburg equation, J. Phys. A: Math. Gen. 25, L1095-L1103, 1992.

25. Wepener V, Euler N, van Vuren J H J, du Preez H H and Köhler A, The development of an aquatic toxicity index as a tool in the operational management of water quality in the Olifants River (Kruger National Park) KOEDOE 35/2, 1-9, 1992.

26. Steeb W-H, Euler N, and Hereman W, A note on the Zakharov equation and Lie symmetry vector fields, Nuovo Cimento 107B, 1211-1213, 1992.

27. Steeb W-H and Euler N, Nonlinear evolution equations and Painlev'e test in Computational and Applied Mathematics II: Differential Equations Sel. Rev. Pap. IMACS 13th World Congr., Dublin/Irel., 227-236, 1992.

28. Euler N, Shul'ga M. W and Steeb W-H, Lie symmetries and Painlev'e test for explicitly space- and time-dependent nonlinear wave equations, J. Phys. A:Math. Gen. 26, L307-L313, 1993.

29. Euler N and Steeb W-H, Nonlinear differential equations, Lie symmetries and the Painlev'e test, in Modern Group Analysis, ed. Ibragimov N.H, Torrisi M. and Valenti A, Kluwer Academic Publishers: Dortrecht, 1993.

30. Steeb W-H and Euler N, Externally driven nonlinear oscillator, Painlev'e test, first integrals and Lie symmetries, Z. Naturforsch. 48a, 1993.

31. Euler N and Köhler A and Fushchich W.I, Q-symmetry generators and exact solutions for nonlinear heat conduction, Physica Scripta, 49, 518-524, 1994.

32. Euler N and Euler M, Symmetry properties of the approximations of multidimensional generalized van der Pol equations, J. Nonlinear Math. Phys.,1, 41-59, 1994.

33. Euler M, Euler N and Köhler A, On the construction of approximate solutions for a multidimensional nonlinear heat equation, J. Phys. A: Math. Gen.,27, 2083-2092, 1994.

34. Euler N, Euler M and Köhler A, Conditional and approximate symmetries for a generalized van der Pol equation, J. Lie Groups and their Appl., 1, 79-94, 1994.

35. Euler N, Painlev'e analysis and conditional auto-Bäcklund transformations for a two-dimensional Boltzmann model, Proceedings of the Ukrainian Academy of Sciences, 8, 42-48, 1994.

36. Euler M, Euler N, Zachary W.W., Mahmood M.F. and Gill T.L, Symmetry classification for a coupled nonlinear Schrödinger equation, J. Nonlinear Math. Phys., 1, 358-379, 1994.

37. Basarab-Horwath P, Euler N, Euler M and Fushchych W I Amplitude-phase representation for solutions of nonlinear d'Alembert equations, J. Phys. A: Math. Gen., 28, 6193-6201, 1995.

38. Euler N and Euler M, Madelung representation for complex nonlinear d'Alembert equation in n-dimensional Minkowski space, J. Nonlinear Math. Phys., 2, 292-300, 1995.

39. Euler N Transformation properties of x''+f_1(t)x'+f_2(t)x+f_3(t)x^n=0 , J. Nonlinear Math. Phys., 4, 310-338, 1997.

40. Euler M, Euler N and O. Lindblom Symmetry for a class of explicitly space- and time-dependent (1+1)-dimensional wave equations, Proceedings of the Second International Conference: Symmetry in Nonlinear Mathematical Physics, Vol. 1 70-78, 1997.

41. Euler N, Lindblom O., Euler M and Persson L-E The higher dimensional Bateman equation and Painlev'e analysis of nonintegrable wave equations, Proceedings of the Second International Conference: Symmetry in Nonlinear Mathematical Physics, Vol. 1 185-192, 1997.

42. Euler M, Euler N and Lindblom O. Explicitly space- and time-dependent d'Alembert equations with symmetries, Int. J. Mod. Phys. A 14, 4189 - 4200, 1999.

43. Euler N and Lindblom O, n-Dimensional Bateman equation and the Painlev'e analysis of wave equations Int. J. Diff. Eqs. and Appl., 1, 205-223, 2000

44. Euler N, Gandarias M L, Euler M and Lindblom O, Auto-hodograph transformations for a hierarchy of nonlinear evolution equations, J. Math. Anal. Appl. 257, 21-28, 2001.

45. Euler N and Lindblom O, On discrete velocity Boltzmann equations and the Painleve analysis, Nonlinear Analysis: Theory, Methods & Applications 47 (2), 1407-1412, 2001

46. Euler M and Euler N, n-Dimensional real wave equations and the d'Alembert-Hamilton system, Nonlinear Analysis: Theory, Methods & Applications 47 (8), 5125-5133, 2001.

47. Euler N and Euler M, A tree of linearisable second-order evolution equations by generalised hodograph transformations , J. Nonlinear Math. Phys. 8, 342-362, 2001.

48. Lindblom O and Euler N, Solutions of Discrete-Velocity Bolzmann Equations via Bateman and Riccati Equations , Theoretical and Mathematical Physics 131, 595--608, 2002.

49. Euler N, Wolf T, Leach P G L and Euler M, Linearisable Third Order Ordinary Differential Equations and Generalised Sundman Transformations: The Case X'''=0 , Acta Appl. Math. 76, 89--115, 2003.

50. Euler M, Euler N, Petersson N, Linearisable Hierarchies of Evolution Equations in (1+1) Dimensions, Stud. Appl. Math., 111, 315--337, 2003.

51. Euler N and Leach P G L, First Integrals and Reduction of a Class of Nonlinear Higher Order Ordinary Differential Equations, J Math. Anal. Appl. 287 (2), 473--486, 2003.

52. Petersson N, Euler N, and Euler M, Recursion Operators for a Class of Integrable Third-Order Evolution Equations, Stud. Appl. Math., 112, 201--225, 2004.

53. Euler N and Euler M, Sundman Symmetries of Nonlinear Second-Order and Third-Order Ordinary Differential Equations, J. Nonlinear Math. Phys., 11, 399--421, 2004.

54. Euler M, Euler N and Leach PGL, The Riccati and Ermakov-Pinney Hierarchies , J. Nonlinear Math. Phys., 14, 290--302, 2007

55. Euler M, Euler N, A Strömberg and E Åström, Transformation between a Generalised Emden-Fowler Equation and the First Painlev\'e Transcendent, Math. Meth. Appl. Sci. 30, 2121--2124, 2007

56. Euler M and Euler N, Second-order recursion operators of third-order evolution equations with fourth-order integrating factors, J. Nonlinear Math. Phys.,14, 313-315, 2007

57. F Calogero, M Euler and N Euler, New evolution PDEs with many isochronous solutions, J. Math. Anal. and Appl., 353, 481-488, 2009

58. N Euler and PGL Leach, Aspects of proper differential sequences of ordinary differential equations. Theoretical and Mathematical Physics, 159, 474-487, 2009.

59. M Euler, N Euler and S Lundberg, On reciprocal-B\"acklund transformations of autonomous evolution equations, Theoretical and Mathematical Physics, 159, 770-778, 2009

60. N Euler and M Euler, On nonlocal symmetries, nonlocal conservation laws and nonlocal transformations of evolution equations: Two linearisable hierarchies, J. Nonlinear Math. Phys., 16, 489-504, 2009.

61. P G L Leach and N Euler, A novel Riccati sequence, J. Nonlinear Math. Phys. 16 Suppl., 157-164, 2009.

62. N Euler and M Euler, Multipotentialisation and iterating-solution formulae: The Krichever-Novikov equation, J. Nonlinear Math. Phys. 16 Suppl., 93-106, 2009.

63. PGL Leach, R R Warne, N Caister, V Naicker and N Euler, Symmetries, Integrals and Solutions of Ordinary Differential Equations of Maximal Symmetry, Proc. Indian Acad. Sci (Math. Sci.) 120 No. 1 (February 2010), 113-130, 2010.

64. M Euler, N Euler and PGL Leach, Properties of the Calogero-Degasperis-Ibragimov-Shabat differential sequence, Lobachevskii Journal of Mathematics 32 No. 1, 61-69, 2011.

65. N Euler and M Euler, The converse problem for the multipotentialisation of evolution equations and systems, J. Nonlinear Math. Phys. 18 Suppl. 1, 77-105, 2011.

66. M Euler and N Euler, A class of semilinear fifth-order evolution equations: Recursion operators and multipotentialisations, J. Nonlinear Math. Phys. 18 Suppl. 1, 61-75, 2011.

67. M Euler and N Euler, Integrating factors and conservation laws for some Camassa-Holm type equations, Commun. Pure Appl. Anal., 11, 1421-1430, 2012.

68. M Euler, N Euler and T Wolf, The two-component Camassa-Holm equations CH(2,1) and CH(2,2): First-order integrating factors and conservation laws, J. Nonlinear Math. Phys., 19 Suppl. 1, 1240002 (10 pages), 2012.

69. N Euler and N Euler, An alternate view on symmetries of second-order linearisable ordinary differential equations, Lobachevskii Journal of Mathematics, 33, 191-194, 2012.

70. N Euler, Linear operators and the general solution of elementary linear ordinary differential equations without Ans\"atze, Community of Ordinary Differential Equations Educators, CJ12-1802 , [Visit C-ODE-E ] May 2012.

71. M Euler and N Euler, Invariance of the Kaup-Kupershmidt equation and triangular auto-B\"acklund transformations, J. Nonlinear Math. Phys., 19, 1220001-1-7, 2012.

72. M Euler, N Euler and M.C. Nucci, On nonlocal symmetries generated by recursion operators: second-order evolution equations, Discrete and Continuous Dynamical Systems: Series A, 37 nr. 8, 4239-4247, 2017.

73. M Euler, N Euler and E G Reyes, Multipotentialisation and nonlocal symmetries: Kupershmidt, Kaup-Kupershmidt and Sawada-Kotera equations, J. Nonlinear Math. Phys., 24 nr. 3, 303-314, 2017.

74. M Euler and N Euler, Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies In: Nonlinear Systems and Their Remarkable Mathematical Structures, Norbert Euler (ed), CRC Press, Boca Raton, USA, 317-351, 2018
 



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