研究者業績

薩摩 順吉

サツマ ジュンキチ  (SATUMA JUNKICHI)

基本情報

所属
武蔵野大学 工学部 数理工学科 教授
学位
工学修士(京都大学大学院)
工学博士(京都大学大学院)

J-GLOBAL ID
201701011554992865
researchmap会員ID
B000271159

論文

 177
  • N. Mimura, J. Satsuma, A. Ramani, B. Grammaticos
    Journal of Mathematical Physics 54(2) 23504 2013年2月5日  
    We present the singularity analysis of the ultradiscrete analogue of linearisable mappings of Quispel-Roberts-Thompson (QRT) type. The ultradiscretisation method used here is one which keeps track of signs and thus can be applied without the positivity restrictions of the classical ultradiscretisation approach. We show that in all cases the mappings possess confined singularities. The same is true for two non-autonomous equations, which are equally linearisable in the discrete case. We construct explicitly the solutions of the ultradiscrete mappings analysed here. © 2013 American Institute of Physics.
  • A. Ramani, B. Grammaticos, J. Satsuma
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 45(36) 365202-365202 2012年9月  
    We examine a class of second-order mappings which can be integrated by reduction to a linear equation. These mappings have been identified in our previous works where we have precisely shown how to obtain their linearization. The mappings belonging to this class are referred to as 'linearizable mappings of the third kind'. We construct their explicit solution and obtain, for all of them, an invariant of QRT aspect but which is non-autonomous. We show that some of these 'third-kind' mappings are related to another class of linearizable mappings, known as mappings of Gambier type, from which they are obtained through a (discrete) derivative with respect to a parameter.
  • Shin Isojima, Junkichi Satsuma, Tetsuji Tokihiro
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 45(15) No.15 2012年4月  
    Ultradiscrete Ai and Bi functions are directly derived through the ultradiscrete limit from q-difference analogues of the Ai and Bi functions, respectively. An infinite number of identities among the number of restricted partitions are obtained as by-products. A direct relationship between a class of special solutions for the ultradiscrete Painleve II equation and those of the q-Painleve II equation which have a determinantal structure is also established.
  • N. Mimura, S. Isojima, M. Murata, J. Satsuma, A. Ramani, B. Grammaticos
    JOURNAL OF MATHEMATICAL PHYSICS 53(2) 023510-023510 2012年2月  
    Ultradiscrete singularity confinement test, which is an integrability detector for ultradiscrete equations with parity variables, is applied to various ultradiscrete equations. The ultradiscrete equations exhibit singularity structures analogous to those of the discrete counterparts. Exact solutions to linearisable ultradiscrete equations are also constructed to explain the singularity structures. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3682229]
  • R.Willox, J.Satsuma, A.Ramani, B.Grammaticos
    Contemporary Mathematics Vol.580 135-155 2012年  

MISC

 24
  • M. Murata, J. Satsuma, A. Ramani, B. Grammaticos
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 43(31) 2010年8月  
    We present a systematic approach to the construction of discrete analogues for differential systems. Our method is tailored to first-order differential equations and relies on a formal linearization, followed by a Pade-like rational approximation of an exponential evolution operator. We apply our method to a host of systems for which there exist discretization results obtained by what we call the 'intuitive' method and compare the discretizations obtained. A discussion of our method as compared to one of the Mickens is also presented. Finally we apply our method to a system of coupled Riccati equations with emphasis on the preservation of the integrable character of the differential system.
  • A. Ramani, B. Grammaticos, J. Satsuma, R. Willox
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42(28) 282002 2009年7月  
    We examine two integrable discrete lattice equations obtained by Levi and Yamilov. We show that the first one is a form of the lattice KdV equation already obtained by Hirota and Tsujimoto, while the second one is a discrete form of mKdV. We present the Miura transformations between the various equations involved, including the more familiar potential form of the lattice mKdV.
  • A. Ramani, B. Grammaticos, J. Satsuma, R. Willox
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42(28) 282002 2009年7月  
    We examine two integrable discrete lattice equations obtained by Levi and Yamilov. We show that the first one is a form of the lattice KdV equation already obtained by Hirota and Tsujimoto, while the second one is a discrete form of mKdV. We present the Miura transformations between the various equations involved, including the more familiar potential form of the lattice mKdV.
  • A. Ramani, B. Grammaticos, J. Satsuma
    CHAOS SOLITONS & FRACTALS 40(1) 491-496 2009年4月  
    We present two models for an epidemic where the individuals are infective over it fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based oil it delay-difference scheme. We show that, as a function of the delay (which corresponds to the Period of infectiveness) the percentage of non-infected population varies over a wide range. We present also a variant of our model where the recovery rate follows a Poisson law and obtain it discrete version of the SIR model. We estimate the percentage of non-infected population in the two models, show that they lead to almost the same values and present an explanation of this fact. The second model is based oil the assumption that the infection is spread by carriers. Under the hypothesis that the carriers are relatively long-lived, and that the number of the infected ones is a relatively small fraction of the total population of potential carriers, we show that the model reduces to the same version of the discrete SIR obtained by our first model. (C) 2007 Elsevier Ltd. All rights reserved.
  • A. Ramani, B. Grammaticos, J. Satsuma
    CHAOS SOLITONS & FRACTALS 40(1) 491-496 2009年4月  
    We present two models for an epidemic where the individuals are infective over it fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based oil it delay-difference scheme. We show that, as a function of the delay (which corresponds to the Period of infectiveness) the percentage of non-infected population varies over a wide range. We present also a variant of our model where the recovery rate follows a Poisson law and obtain it discrete version of the SIR model. We estimate the percentage of non-infected population in the two models, show that they lead to almost the same values and present an explanation of this fact. The second model is based oil the assumption that the infection is spread by carriers. Under the hypothesis that the carriers are relatively long-lived, and that the number of the infected ones is a relatively small fraction of the total population of potential carriers, we show that the model reduces to the same version of the discrete SIR obtained by our first model. (C) 2007 Elsevier Ltd. All rights reserved.
  • RIMS Kokyuroku Bessatsu B13 85-93 2009年  
  • S. Isojima, T. Konno
    RIMS 講究録別冊 B13 85-93 2009年  
  • N Mimura, S Isojima, M Murata
    J. Phys. A 42(31) 315206 2009年  
  • A. Ramani, B. Grammaticos, J. Satsuma, R. Willox
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 41(20) 2008年5月  
    We show that a discretization of a continuous system may entail 'hidden' delays and thus introduce instabilities. In this case, while the continuous system has an attractive fixed point, the instabilities present in the equivalent discrete one may lead to the appearance of a limit cycle. We explain that it is possible, thanks to the proper staggering of the discrete variables, to eliminate the hidden delay. However, in general, other instabilities may appear in the discrete system which can even lead to chaotic behaviour.
  • S. Isojima, S. Kubo, M. Murata
    J. Phys. A 2008年  
  • A. Ramani, B. Grammaticos, R. Willox
    Can't open convert table.(java.lang.NullPointerException) 2008年  
  • R. Willox, A. Ramani, J. Satsuma, B. Grammaticos
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 385(2) 473-486 2007年11月  
    We examine the transition between discrete and ultradiscrete (cellular-automaton-like) systems, the dynamics of which exhibit limit cycles. Motivated by results obtained previously for three-dimensional systems, we consider here a more manageable two-dimensional model. We show that one can follow the changes in dynamics of the system when a parameter that tunes the discrete-ultradiscrete transition is varied. In particular we explain the phenomenon of the splitting of a discrete limit cycle to a profusion of periodic orbits at the ultradiscrete limit. (C) 2007 Elsevier B.V. All rights reserved.
  • R. Willox, A. Ramani, J. Satsuma, B. Grammaticos
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 385(2) 473-486 2007年11月  
    We examine the transition between discrete and ultradiscrete (cellular-automaton-like) systems, the dynamics of which exhibit limit cycles. Motivated by results obtained previously for three-dimensional systems, we consider here a more manageable two-dimensional model. We show that one can follow the changes in dynamics of the system when a parameter that tunes the discrete-ultradiscrete transition is varied. In particular we explain the phenomenon of the splitting of a discrete limit cycle to a profusion of periodic orbits at the ultradiscrete limit. (C) 2007 Elsevier B.V. All rights reserved.
  • B. Grammaticos, A. Ramani, V. Papageorgiou, J. Satsuma, R. Willox
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 40(42) 12619-12627 2007年10月  
    We construct special solutions of the Hirota-Miwa equation for which the tau-function is a polynomial in the independent variables. Three different methods are presented: direct construction ( obtained also as a limit of the soliton solutions), and the derivation of the solutions in two different determinant forms, namely Grammian and Casorati. Introducing the appropriate ansatz, we write the Hirota-Miwa equation in a nonlinear form for a single variable. In terms of the latter, the solutions obtained are rational and are reminiscent of the lump solutions for the continuous analogue of the Hirota-Miwa equation, namely the KP equation.
  • B. Grammaticos, A. Ramani, V. Papageorgiou, J. Satsuma, R. Willox
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 40(42) 12619-12627 2007年10月  
    We construct special solutions of the Hirota-Miwa equation for which the tau-function is a polynomial in the independent variables. Three different methods are presented: direct construction ( obtained also as a limit of the soliton solutions), and the derivation of the solutions in two different determinant forms, namely Grammian and Casorati. Introducing the appropriate ansatz, we write the Hirota-Miwa equation in a nonlinear form for a single variable. In terms of the latter, the solutions obtained are rational and are reminiscent of the lump solutions for the continuous analogue of the Hirota-Miwa equation, namely the KP equation.
  • S. Kubo, S. Isojima, M. Murata, J. Satsuma
    Phys. Lett. A 362(5-6) 430-434 2007年  
  • A.S. Carstea, A. Ramani, J. Satsuma, R. Willox, B. Grammaticos
    Physica A 364 276-286 2006年  
  • S. Isojima, M. Murata, A. Nobe, J. Satsuma
    Phys. Lett. A 357(1) 31-35 2006年  
  • A.Ramani, R.Willox, B.Grammaticos, A.S.Carstea, J.Satsuma
    Physica A 347 1-16 2005年3月  
  • B.Grammaticos, A.Ramani, J.Satsuma, R.Willox, A.S.Carstea
    Journal of Nonlinear Mathematical Physics 1 363-371 2005年  
  • R.Willox, J.Satsuma
    Lecture Notes in Physics Discrete Integrable Systems (644) 17-55 2004年  
  • S.Isojima, M.Murata, A.Nobe, J.Satsuma
    Phys. Lett. A 331(6) 378-386 2004年  

書籍等出版物

 16

講演・口頭発表等

 12