Similarity solutions of stochastic nonlinear parabolic equations

A novel statistical technique introduced by Besieris is used to study solutions of the nonlinear stochastic complex parabolic equation in the presence of two profiles. Specifically, the randomly modulated linear potential and the randomly perturbed quadratic focusing medium. In the former, a class of solutions is shown to admit an exact statistical description in terms of the moments of the wave function. In the latter, all even-order moments are computed exactly, whereas the odd-order moments are solved asymptotically. Lastly, it is shown that this statistical technique is isomorphic to mappings of nonconstant coefficient partial differential equations to constant coefficient equations. A generalization of this mapping and its inherent restrictions are discussed.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Electrical Engineering

Department dc:contributor.department

Electrical Engineering

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1987

Author dc:creator

• Sockell, Michael Elliot

Chair dc:contributor.committeechair

• Bevan, David R.

Committee members dc:contributor.committeemember

• Davis, William A.
• Kohler, Werner
• de Wolf, David A.
• Nayfeh, Ali

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Handle dc:identifier.uri

http://hdl.handle.net/10919/49898

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/49898