ON FOKKER-PLANCK AND LINEARIZED KORTEWEG-DE VRIES TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLES

In the present work, we construct solutions to a Fokker-Planck type equation with real time variable and complex spatial variable, and prove some properties. The equations are obtained from the complexification of the spatial variable by two different methods. Firstly, one complexifies the spatial v...

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Detalles Bibliográficos
Autores principales:	Gal,Ciprian G, Gal,Sorin G
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2013
Materias:	Fokker -Planck equation Korteweg-de Vries equation complex convolution integrals complex spatial variables
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000100003
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spelling	oai:scielo:S0719-064620130001000032018-10-08ON FOKKER-PLANCK AND LINEARIZED KORTEWEG-DE VRIES TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLESGal,Ciprian GGal,Sorin G Fokker -Planck equation Korteweg-de Vries equation complex convolution integrals complex spatial variables In the present work, we construct solutions to a Fokker-Planck type equation with real time variable and complex spatial variable, and prove some properties. The equations are obtained from the complexification of the spatial variable by two different methods. Firstly, one complexifies the spatial variable in the corresponding convolution integral in the solution, by replacing the usual sum of variables (translation) by an exponential product (rotation). Secondly, one complexifies the spatial variable directly in the corresponding evolution equation and then one searches for analytic solutions. These methods are also applied to a linear evolution equation related to the Korteweg-de Vries equation.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.15 n.1 20132013-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000100003en10.4067/S0719-06462013000100003
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Fokker -Planck equation Korteweg-de Vries equation complex convolution integrals complex spatial variables
spellingShingle	Fokker -Planck equation Korteweg-de Vries equation complex convolution integrals complex spatial variables Gal,Ciprian G Gal,Sorin G ON FOKKER-PLANCK AND LINEARIZED KORTEWEG-DE VRIES TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLES
description	In the present work, we construct solutions to a Fokker-Planck type equation with real time variable and complex spatial variable, and prove some properties. The equations are obtained from the complexification of the spatial variable by two different methods. Firstly, one complexifies the spatial variable in the corresponding convolution integral in the solution, by replacing the usual sum of variables (translation) by an exponential product (rotation). Secondly, one complexifies the spatial variable directly in the corresponding evolution equation and then one searches for analytic solutions. These methods are also applied to a linear evolution equation related to the Korteweg-de Vries equation.
author	Gal,Ciprian G Gal,Sorin G
author_facet	Gal,Ciprian G Gal,Sorin G
author_sort	Gal,Ciprian G
title	ON FOKKER-PLANCK AND LINEARIZED KORTEWEG-DE VRIES TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLES
title_short	ON FOKKER-PLANCK AND LINEARIZED KORTEWEG-DE VRIES TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLES
title_full	ON FOKKER-PLANCK AND LINEARIZED KORTEWEG-DE VRIES TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLES
title_fullStr	ON FOKKER-PLANCK AND LINEARIZED KORTEWEG-DE VRIES TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLES
title_full_unstemmed	ON FOKKER-PLANCK AND LINEARIZED KORTEWEG-DE VRIES TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLES
title_sort	on fokker-planck and linearized korteweg-de vries type equations with complex spatial variables
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2013
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000100003
work_keys_str_mv	AT galcipriang onfokkerplanckandlinearizedkortewegdevriestypeequationswithcomplexspatialvariables AT galsoring onfokkerplanckandlinearizedkortewegdevriestypeequationswithcomplexspatialvariables
_version_	1714206781061726208

ON FOKKER-PLANCK AND LINEARIZED KORTEWEG-DE VRIES TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLES

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