Kenji Kajiwara | Last modified date：2023.06.14 |

Professor /
Division of Applied Mathematics /
Institute of Mathematics for Industry

**Papers**

1. | Sebastian Elias Graiff-Zurita, Kenji Kajiwara, Kenjiro T. Miura, Fairing of planar curves to log-aesthetic curves, Japan Journal of Industrial and Applied Mathematics, 10.1142/S2661335222500071, 40, 1203-1219, 2023.03. |

2. | Sebastian Elias Graiff-Zurita, Kenji Kajiwara and Toshitomo Suzuki, Fairing of Discrete Planar Curves by Integrable Discrete Analogue of Euler's Elasticae, International Journal of Mathematics for Industry, 10.1142/S2661335222500071, 14, 1, 225007, 2023.03. |

3. | Sebastián Elías Graiff-Zurita, Kenji Kajiwara, Fairing of discrete planar curves by discrete Euler's elasticae, JSIAM Letters, https://doi.org/10.14495/jsiaml.11.73, 11, 73-76, 2019.12. |

4. | Shizuo Kaji, Hyeongki Park, Kenji Kajiwara, Linkage Mechanisms Governed by Integrable Deformations of Discrete Space Curves, Nonlinear Systems and Their Remarkable Mathematical Structures Volume 2, 356-381, 2020.01, A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage mechanisms which consist of n-copies of a rigid body joined together by hinges to form a ring. Each hinge joint has its own axis of revolution and rigid bodies joined to it can be freely rotated around the axis. The family includes the famous threefold symmetric Bricard6R linkage also known as the Kaleidocycle, which exhibits a characteristic "turning over" motion. We can model such a linkage as a discrete closed curve in ℝ3 with a constant torsion up to sign. Then, its motion is described as the deformation of the curve preserving torsion and arc length. We describe certain motions of this object that are governed by the semi-discrete mKdV equations, where infinitesimally the motion of each vertex is confined in the osculating plane.. |

5. | Hyeongki Park, Jun-ichi Inoguchi, Kenji Kajiwara, Ken-ichi Maruno, Nozomu Matsuura, Yasuhiro Ohta, Isoperimetric deformations of curves on the Minkowski plane, International Journal of Geometric Methods in Modern Physics, 10.1142/S0219887819501007, 16, 1950100(20 pages), 2019.06. |

6. | Sampei Hirose, Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta, Discrete local induction equation, Journal of Integrable Systems, 10.1093/integr/xyz003, 4, 1, xyz003, 2019.06, [URL]. |

7. | Hyeongki Park, Kenji Kajiwara, Takashi Kurose, Nozomu Matsuura, Defocusing mKdV flow on centroaffine plane curves, JSIAM Letters, 10.14495/jsiaml.10.25, 10, 25-28, 2018.07. |

8. | Dimetre Triadis, Philip Broadbridge, Kenji Kajiwara, Ken Ichi Maruno, Integrable Discrete Model for One-Dimensional Soil Water Infiltration, Studies in Applied Mathematics, 10.1111/sapm.12208, 140, 4, 483-507, 2018.05, We propose an integrable discrete model of one-dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection–diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time-dependent flux term by the hodograph transformation. We construct a discrete model preserving the underlying integrability, which is formulated as the self-adaptive moving mesh scheme. The discretization is based on linearizability of the Burgers equation to the linear diffusion equation, but the naïve discretization based on the Euler scheme which is often used in the theory of discrete integrable systems does not necessarily give a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model that produces solutions with similar accuracy to direct computation on the original nonlinear equation, but with clear benefits regarding computational cost.. |

9. | Kenjiro T. Miura, Sho Suzuki, R. U. Gobithaasan, Shin Usuki, Jun ichi Inoguchi, Masayuki Sato, Kenji Kajiwara, Yasuhiro Shimizu, Fairness metric of plane curves defined with similarity geometry invariants, Computer-Aided Design and Applications, 10.1080/16864360.2017.1375677, 15, 2, 256-263, 2018.03, A curve is considered fair if it consists of continuous and few monotonic curvature segments. Polynomial curves such as Bézier and B-spline curves have complex curvature function, hence the curvature profile may oscillate easily with a little tweak of control points. Thus, bending energy and shear deformation energy are common fairness metrics used to produce curves with monotonic curvature profiles. The fairness metrics are used not just to evaluate the quality of curves, but it also aids in reaching to the final design. In this paper, we propose two types of fairness metric functionals to fair plane curves defined by the similarity geometry invariants, i.e. similarity curvature and its reciprocal to extend a variety of aesthetic fairing metrics. We illustrate numerical examples to show how log-aesthetic curves change depending on σ and G^{1} constraints. We extend LAC by modifying the integrand of the functionals and obtain quasi aesthetic curves. We also propose σ-curve to introduce symmetry concept for the log-aesthetic curve.. |

10. | Jun ichi Inoguchi, Kenji Kajiwara, Kenjiro T. Miura, Masayuki Sato, Wolfgang K. Schief, Yasuhiro Shimizu, Log-aesthetic curves as similarity geometric analogue of Euler's elasticae, Computer Aided Geometric Design, 10.1016/j.cagd.2018.02.002, 61, 1-5, 2018.03, In this paper we consider the log-aesthetic curves and their generalization which are used in CAGD. We consider those curves under similarity geometry and characterize them as stationary integrable flow on plane curves which is governed by the Burgers equation. We propose a variational formulation of those curves whose Euler–Lagrange equation yields the stationary Burgers equation. Our result suggests that the log-aesthetic curves and their generalization can be regarded as the similarity geometric analogue of Euler's elasticae.. |

11. | Nalini Joshi, Kenji Kajiwara, Tetsu Masuda, Nobutaka Nakazono, Yang Shi, Geometric description of a discrete power function associated with the sixth Painlevé equation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 10.1098/rspa.2017.0312, 473, 2207, 2017.11, In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with W (3A^{(1)} _{1} ) symmetry. By constructing the action of W (3A^{(1)} _{1} ) as a subgroup of W (D^{(1)} _{4} ), i.e. the symmetry group of P_{VI}, we show how to relate W (D^{(1)} _{4} ) to the symmetry group of the lattice. Moreover, by using translations in W (3A^{(1)} _{1} ), we explain the odd–even structure appearing in previously known explicit formulae in terms of the t function.. |

12. | Hele-Shaw problem with surface tension. |

13. | Vladimir Bazhanov, Patrick Dorey, Kenji Kajiwara, Kanehisa Takasaki, Call for papers Special issue on fifty years of the Toda lattice, Journal of Physics A: Mathematical and Theoretical, 10.1088/1751-8121/aa748f, 50, 31, 2017.01. |

14. | Kenji Kajiwara, Masatoshi Noumi, Yasuhiko Yamada, Geometric aspects of Painlevé equations, Journal of Physics A: Mathematical and Theoretical, 10.1088/1751-8121/50/7/073001, 50, 7, 2017.01, In this paper a comprehensive review is given on the current status of achievements in the geometric aspects of the Painlev equations, with a particular emphasis on the discrete Painlevï¿½ equations. The theory is controlled by the geometry of certain rational surfaces called the spaces of initial values, which are characterized by eight point configuration on P1xP1. We give a systematic description of the equations and their various properties, such as affine Weyl group symmetries, hypergeometric solutions and Lax pairs under this framework, by using the language of Picard lattice and root systems. We also provide with a collection of basic data; equations, point configurations/root data, Weyl group representations, Lax pairs, and hypergeometric solutions of all possible cases.. |

15. | Sampei Hirose, Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta, dNLS flow on discrete space curves, Mathematics for Industry, 10.1007/978-981-10-1076-7, 24, 137-149, 2016.06. |

16. | Kenji Kajiwara, Toshinobu Kuroda, Nozomu Matsuura, Isogonal deformation of discrete plane curves and discrete Burgers hierarchy, Pacific Journal of Mathematics for Industry, 10.1186/s40736-016-0022-z, 8:3, 2016.03. |

17. | Kenji Kajiwara, Saburo Kakei, Toda lattice hierarchy and Goldstein-Petrich flows for plane curves, Commentarii Mathematici Univ. St. Pauli, 63, 29-45, 2015.10. |

18. | Hisashi Ando, Mike Hay, Kenji Kajiwara, Tetsu Masuda, Explicit formula and extension of the discrete power function associated with the circle patterns of Schramm type, Mathematics for Industry, 10.1007/978-4-431-55007-5_15, 18, 19-32, 2015.09. |

19. | Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta, Discrete Isoperimetric Deformation of Discrete Curves, Mathematics for Industry, 10.1007/978-4-431-55007-5_15, 4, 111-122, 2014.09. |

20. | Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta, Discrete models of isoperimetric deformation of plane curves, Mathematics for Industry, doi:10.1007/978-4-431-55060-0_7, 5, 89-100, 2014.06. |

21. | Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Kobe University, Discrete mKdV and discrete sine-Gordon flows on discrete space curves, Journal of Physics A: Mathematical and Theoretical, doi:10.1088/1751-8113/47/23/235202, 47, 23, 235202, 2014.05. |

22. | B.F. Feng, J. Inoguchi, Kenji Kajiwara, K. Maruno, Y. Ohta, Integrable discretizations of the Dym equation, Frontiers of Mathematics in China, 10.1007/s11464-013-0321-y, 8, 5, 1017-1029, 2013.10. |

23. | K. Maruno, B.F. Feng, J. Inoguchi, K. Kajiwara, Y. Ohta, Semi-discrete analogues of the elastic beam equation and the short pulse equation, Proceedings of 2013 International Symposium on Nonlinear Theory and its Applications, 278-281, 2013.07. |

24. | Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta, Motion and Bäcklund transformations of discrete plane curves, Kyushu Journal of Mathematics, doi:10.2206/kyushujm.66.303, 66, 2, 303-324, 2012.10, We construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently. Explicit formulas in terms of the τ function are presented. Transformation theory of the motions of both smooth and discrete curves is developed simultaneously.. |

25. | Jun-ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta, Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves, Journal of Physics A: Mathematical and Theoretical, doi:10.1088/1751-8113/45/4/045206, 45, 045206(16pp), 2012.01, We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the τ function are presented. Ba ̈cklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation.. |

26. | Bao-Feng Feng, Jun-ichi Inoguchi, Kenji Kajiwara, Ken-ichi Maruno, Yasuhiro Ohta, Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves, Journal of Physics A: Mathematical and Theoretical, doi:10.1088/1751-8113/44/39/395201, 44, 39, 395201, 2011.09. |

27. | Mike Hay, Kenji Kajiwara and Tetsu Masuda, Bilinearization and special solutions to the discrete Schwarzian KdV equation, Journal of Math-for-Industry, 3, 2011A, 53-62, 2011.04. |

28. | Kenji Kajiwara, Nobutaka Nakazono and Teruhisa Tsuda, Projective reduction of the discrete Painlevé system of type (A2+A1)(1), International Mathematical Research Notices, 10.1093/imrn/rnq089, Vol. 2010, article ID: rnq089, 2010.05. |

29. | Ken-ichi Maruno and Kenji Kajiwara, The discrete potential Boussinesq equation and its multisoliton solutions , Applicable Analysis, 10.1080/00036810903569473 , 89, 4, 593-609, 2010.04. |

30. | Kenji Kajiwara and Yasuhiro Ohta, Bilinearization and Casorati determinant solutions to non-autonomous 1 + 1 dimensional discrete soliton equations, RIMS Kokyuroku Bessatsu , B13, 53-74, 2009.11. |

31. | Kenji Kajiwara, Masanobu Kaneko, Atsushi Nobe and Teruhisa Tsuda, Ultradiscretization of a solvable two-dimensional chaotic map assciated with the Hesse cubic curve , Kyushu Journal of Mathematics, 63巻2号315-338ページ, 2009.09. |

32. | Kenji Kajiwara, Atsushi Nobe and Teruhisa Tsuda, Ultradiscretization of solvable one-dimensional chaotic maps, Journal of Physics A: Mathematical and Theoretical, 41巻，395202, 2008.09. |

33. | Kenji Kajiwara and Yasuhiro Ohta, Bilinearization and Casorati determinant solution to the non-autonomous discrete KdV equation, Journal of the Physical Society of Japan, 77巻, 054004, 2008.05. |

34. | Kenji Kajiwara, Marta Mazzocco and Yasuhiro Ohta, A remark on the Hankel determinant formula for solutions of the Toda equation, Journal of Physics A: Mathematical and Theoretical, 40巻，12661-12675, 2007.10, [URL]. |

35. | Taro Hamamoto and Kenji Kajiwara, Hypergeometric solutions to the q-Painleve equation of type A_4^{(1)}, Journal of Physics A: Mathematical and Theoretical, 40巻，12509-12524, 2007.10, [URL]. |

36. | Kenji Kajiwara, Tetsu Masuda, Masatoshi Noumi, Yasuhiro Ohta and Yasuhiko Yamada, Point configurations, Cremona transformations and the elliptic difference Painleve equation, Séminaires et Congrès , 14巻，175-204., 2007.08. |

37. | Nalini Joshi, Kenji Kajiwara and Marta Mazzocco, Generating function associated with the Hankel determinant formula for solutions of the Painleve IV equation, Funkcialaj Ekvacioj, 49(3), 451-468, 2006.12. |

38. | Taro Hamamoto, Kenji Kajiwara and Nicholas S. Witte, Hypergeometric solutions to the q-Painleve equation of type $(A_1+A_1')^{(1)}$, Interenational Mathematics Research Notices, 2006, Article ID 84619, 2006.10. |

39. | Hiromichi Goto and Kenji Kajiwara, Generating Function Related to the Okamoto Polynomials for the Painlev\'e IV Equation, Bulletin of the Australian Mathematical Society, 71, 3, 517-526, Vol.71(3)(2005) 517-526, 2005.08. |

40. | Kenji Kajiwara and Atsushi Mukaihira, Soliton Solutions for the Non-autonomous Discrete-time Toda Lattice Equation, Journal of Physics A: Mathematical and General, 10.1088/0305-4470/38/28/008, 38, 28, 6363-6370, Vol.38(28) (2005) 6363-6370, 2005.06. |

41. | Nalini Joshi, Kenji Kajiwara and Marta Mazzocco, Generating Function Associated with the Determinant Formula for the Solutions of the Painlev\'e II Equation, Ast\'erisque, 297, 67-78, Vol.274(2004) 67-78, 2005.06. |

42. | Kenji Kajiwara, Tetsu Masuda, Masatoshi Noumi, Yasuhiro Ohta and Yasuhiko Yamada, Cubic Pencils and Painlev\'e Hamiltonians, Funkcialaj Ekvacioj, Vol.48(1) (2005) 147-160, 2005.04. |

43. | Kenji Kajiwara, Tetsu Masuda, Masatoshi Noumi, Yasuhiro Ohta and Yasuhiko Yamada, Construction of Hypergeometric Solutions to the q-Painlev\'e Equations, International Mathematical Research Notices, 24, 1439-1463, Vol.2005(24) (2005) 1439-1463, 2005.01. |

44. | Kenji Kajiwara, Tetsu Masuda, Masatoshi Noumi, Yasuhiro Ohta and Yasuhiko Yamada, Hypergeometric solutions to the q-Painleve equations, International Mathematical Research Notices, 47, 2497-2521, 2004:47 (2004) 2497-2521, 2004.08. |

45. | Kenji Kajiwara, On a q-Painleve III equation.II: rational solutions, Journal of Nonlinear Mathematical Physics, Vol.22 282-303, 2003.08. |

46. | K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta and Y. Yamada, 10E9 solution to elliptic Painleve equation, Journal of Physics A: Mathematica and General, Vol.36 L263-L272, 2003.05. |

47. | Kenji Kajiwara and Kinji Kimura, On a $q$-Painlev\'e III Equation. I: Derivations, Symmetry and Riccati Type Soutions, Journal of Nonlinear Mathematical Physics, Vol.10, 86-102, 2003.02. |

48. | Kenji Kajiwara, Masatoshi Noumi and Yasuhiko Yamada, q-Painlev\'e Systems Arising from q-KP Hierarchy, Letters in Mathematical Physics, 10.1023/A:1022216308475, 62, 3, 259-268, Vol.62, 259-268., 2002.12. |

49. | Kenji Kajiwara, Masatoshi Noumi and Yasuhiko Yamada, Discrete Dynamical Systems with W(A{(1)}{m-1} x A{(1)}_{n-1}) Symmetry, Letters in Mathematical Physics, 10.1023/A:1016298925276, 60, 3, 211-219, Vol.60, 211-219, 2002.06. |

50. | Katsunori Iwasaki, Kenji Kajiwara and Toshiya Nakamura, Generating Function Associated with the Rational Solutions of the Painlev\'e II Equation, Journal of Physics A: Mathematical and General, 10.1088/0305-4470/35/16/101, 35, 16, L207-L211, Vol.35, L207-L211, 2002.04. |

51. | Tetsu Masuda, Yasuhiro Ohta and Kenji Kajiwara, A Determinant Formula for a Class of Rational Solutions of Painlev\'e V Equation, Nagoya Mathematical Journal, 168, 1-25, Vol. 168, 1-25., 2002.01. |

52. | Kenji Kajiwara, Masatoshi Noumi and Yasuhiko Yamada, A Study on the Fourth q-Painlev\'e Equation, Journal of Physics A: Mathematical and General, Vol.34,8563-8581, 2001.10. |

53. | Kenji Kajiwara, Tetsu Masuda, Masatoshi Noumi, Yasuhiro Ohta and
Yasuhiko Yamada, Determinant Formulas for the Toda and Discrete Toda Equations, Funkcialaj Ekvacioj, Vol. 44,291-307, 2001.08. |

54. | Kenji Kajiwara, Ken-ichi Maruno and Masayuki Oikawa, Biliearization of Discrete Soliton Equations through the Singularity Confinement Test, Chaos, Solitons & Fractals, 10.1016/S0960-0779(98)00265-3, 11, 1-3, 33-39, Vol.11, 33-40., 2000.03. |

55. | Ken-ichi Maruno, Kenji Kajiwara and Masayuki Oikawa, A Note on Integrable Systems Related to Discrete Time Toda Lattice, CRM Proceedings and Lecture Notes, Vol.25, 303-314, 2000.01. |

56. | Kenji Kajiwara and Tetsu Masuda, On the Umemura Polynomials for the Painlev\'e III Equation, Physics Letters A, Vol.260, 462-467, 1999.09. |

57. | Kenji Kajiwara and Tetsu Masuda, A Generalization of Determinant Formulae for the Solutions of Painlev\'e II and XXXIV Equations, Journal of Physics A: Mathematical and General, Vol. 32, 3763-3778, 1999.05. |

58. | Daisuke Takahashi and Kenji Kajiwara, On the Integrability Test for Ultradiscrtete Equations, 京都大学数理解析研究所講究録 1098「離散可積分系の応用数理」, 1-13, 1999.04. |

59. | Yoshimasa Nakamura, Kenji Kajiwara and Hironori Shiotani, On an Integrable Discretization of the Rayleigh Quatient Gradient System and the Power Method with the Optimal Shift, Journal of Computational and Applied Mathematics, Vol.96, 77-90, 1998.09. |

60. | K. M. Tamizhmani, A. Ramani, B. Grammaticos and K. Kajiwara, Coalescense Cascades and Special Function Solutions for the Continuous and Discrete Painlev\'e Equation, Journal of Physics A: Mathematical and General, Vol.31, 5799--5810, 1998.07. |

61. | Ken-ichi Maruno, Kenji Kajiwara and Masayuki Oikawa, Casorati Determinant Solutions for the Discrete Relativistic Toda Lattice Equation, Physics Letters A, 10.1016/S0375-9601(98)00150-9, 241, 6, 335-343, Vol.241, 335-343., 1998.05. |

62. | Kenji Kajiwara and Yasuhiro Ohta, Determinant Structure of the Rational Solutions for the Painlev\'e IV Equation, Journal of Physics A: Mathematical and General, Vol. 31, 2431--2446, 1998.03. |

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