TY - JOUR
T1 - Equilibrium distribution function for kdv and modified kdv solitons in a fluctuating environment
AU - Malomed, B. A.
AU - Flytzanis, N.
PY - 1994/1/10
Y1 - 1994/1/10
N2 - Starting from the Boussinesq equation (BqE) with dissipation and fluctuation terms, modelling several solid-state systems, we get the corresponding Korteweg-de Vries (KdV) equation for the unidirectional waves. Then we derive the Fokker-Planck equation for the amplitude of the KdV soliton, and we find its stationary solution. The solution represents a normalizable distribution function, which up to a pre-exponential factor has the canonical Boltzmann form in terms of the underlying BqE. We have also solved the same problem for the modified Bq/KdV equation.
AB - Starting from the Boussinesq equation (BqE) with dissipation and fluctuation terms, modelling several solid-state systems, we get the corresponding Korteweg-de Vries (KdV) equation for the unidirectional waves. Then we derive the Fokker-Planck equation for the amplitude of the KdV soliton, and we find its stationary solution. The solution represents a normalizable distribution function, which up to a pre-exponential factor has the canonical Boltzmann form in terms of the underlying BqE. We have also solved the same problem for the modified Bq/KdV equation.
UR - http://www.scopus.com/inward/record.url?scp=84956232716&partnerID=8YFLogxK
U2 - 10.1209/0295-5075/25/2/002
DO - 10.1209/0295-5075/25/2/002
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AN - SCOPUS:84956232716
SN - 0295-5075
VL - 25
SP - 87
EP - 91
JO - Journal de Physique (Paris), Lettres
JF - Journal de Physique (Paris), Lettres
IS - 2
ER -