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 -