Abstract
The soliton physics for the propagation of waves is represented by a stochastic model in which the particles of the wave can jump ahead according to some probability distribution. We demonstrate the presence of a steady state (stationary distribution) for the wavelength. It is shown that the stationary distribution is a convolution of geometric random variables. Approximations to the stationary distribution are investigated for a large number of particles. The model is rich and includes Gaussian cases as limit distribution for the wavelength (when suitably normalized). A sufficient Lindeberg-like condition identifies a class of solitons with normal behavior. Our general model includes, among many other reasonable alternatives, an exponential aging soliton, of which the uniform soliton is one special subcase (with Gumbel's stationary distribution). With the proper interpretation, our model also includes the deterministic model proposed in Takahashi and Satsuma [A soliton cellular automaton, J Phys Soc Japan 59 (1990), 3514-3519].
| Original language | English |
|---|---|
| Pages (from-to) | 51-64 |
| Number of pages | 14 |
| Journal | Random Structures and Algorithms |
| Volume | 24 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2004 Jan |
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Keywords
- Limit distribution
- Random structure
- Soliton
- Wave propagation
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Software
- Mathematics(all)
- Applied Mathematics
Cite this
A Stochastic Model for Solitons. / Itoh, Yoshiaki; Mahmoud, Hosam M.; Takahashi, Daisuke.
In: Random Structures and Algorithms, Vol. 24, No. 1, 01.2004, p. 51-64.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A Stochastic Model for Solitons
AU - Itoh, Yoshiaki
AU - Mahmoud, Hosam M.
AU - Takahashi, Daisuke
PY - 2004/1
Y1 - 2004/1
N2 - The soliton physics for the propagation of waves is represented by a stochastic model in which the particles of the wave can jump ahead according to some probability distribution. We demonstrate the presence of a steady state (stationary distribution) for the wavelength. It is shown that the stationary distribution is a convolution of geometric random variables. Approximations to the stationary distribution are investigated for a large number of particles. The model is rich and includes Gaussian cases as limit distribution for the wavelength (when suitably normalized). A sufficient Lindeberg-like condition identifies a class of solitons with normal behavior. Our general model includes, among many other reasonable alternatives, an exponential aging soliton, of which the uniform soliton is one special subcase (with Gumbel's stationary distribution). With the proper interpretation, our model also includes the deterministic model proposed in Takahashi and Satsuma [A soliton cellular automaton, J Phys Soc Japan 59 (1990), 3514-3519].
AB - The soliton physics for the propagation of waves is represented by a stochastic model in which the particles of the wave can jump ahead according to some probability distribution. We demonstrate the presence of a steady state (stationary distribution) for the wavelength. It is shown that the stationary distribution is a convolution of geometric random variables. Approximations to the stationary distribution are investigated for a large number of particles. The model is rich and includes Gaussian cases as limit distribution for the wavelength (when suitably normalized). A sufficient Lindeberg-like condition identifies a class of solitons with normal behavior. Our general model includes, among many other reasonable alternatives, an exponential aging soliton, of which the uniform soliton is one special subcase (with Gumbel's stationary distribution). With the proper interpretation, our model also includes the deterministic model proposed in Takahashi and Satsuma [A soliton cellular automaton, J Phys Soc Japan 59 (1990), 3514-3519].
KW - Limit distribution
KW - Random structure
KW - Soliton
KW - Wave propagation
UR - http://www.scopus.com/inward/record.url?scp=0348199034&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0348199034&partnerID=8YFLogxK
U2 - 10.1002/rsa.10106
DO - 10.1002/rsa.10106
M3 - Article
AN - SCOPUS:0348199034
VL - 24
SP - 51
EP - 64
JO - Random Structures and Algorithms
JF - Random Structures and Algorithms
SN - 1042-9832
IS - 1
ER -