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Journal of Physics A: Mathematical and General Volume 34 Number 48 Create an alert RSS this journal

Shigeki Matsutani 2001 J. Phys. A: Math. Gen. 34 10737 doi:10.1088/0305-4470/34/48/335

The Lotka-Volterra equation over a finite ring Bbb Z/pNBbb Z

Shigeki Matsutani

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Abstract References

The discrete Lotka-Volterra equation over p-adic space was constructed since p-adic space is a prototype of spaces with non-Archimedean valuations and the space given by taking the ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations given in my previous paper (Matsutani S 2001 Int. J. Math. Math. Sci.). In this paper, using the natural projection from a p-adic integer to a ring Bbb Z/pnBbb Z, a soliton equation is defined over the ring. Numerical computations show that it behaves regularly.


PACS

02.10.Hh Rings and algebras

05.45.Yv Solitons

MSC

12Y05 Computational aspects of field theory and polynomials

16P10 Finite rings and finite-dimensional algebras (For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx)

46S10 Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis (See also 12J25, 32P05)

37K40 Soliton theory, asymptotic behavior of solutions

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 48 (7 December 2001)

Received 8 March 2001, in final form 28 August 2001

Published 23 November 2001



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