Geodesic
Special solutions of the Riccati equation with applications to the Gross-Pitaevskii nonlinear PDE
Electronic journal of differential equations, Tome 2010 (2010)
A method for finding solutions of the Riccati differential equation $y' = P(x) + Q(x)y + R(x)y^2$ is introduced. Provided that certain relations exist between the coefficient $P(x), Q(x)$ and $R(x)$, the above equation can be solved in closed form. We determine the required relations and find the general solutions to the aforementioned equation. The method is then applied to the Riccati equation arising in the solution of the multidimensional Gross-Pitaevskii equation of Bose-Einstein condensates by the F-expansion and the balance principle techniques.
Classification : 34A34, 34A05
Keywords: Riccati equation, solutions to Gross-Pitaevskii equation, chirp function 
@article{EJDE_2010__2010__a259,
     author = {Al Bastami,  Anas and Beli\'c,  Milivoj R. and Petrovi\'c,  Nikola Z.},
     title = {Special solutions of the {Riccati} equation with applications to the {Gross-Pitaevskii} nonlinear {PDE}},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1201.34013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a259/}
}
TY  - JOUR
AU  - Al Bastami,  Anas
AU  - Belić,  Milivoj R.
AU  - Petrović,  Nikola Z.
TI  - Special solutions of the Riccati equation with applications to the Gross-Pitaevskii nonlinear PDE
JO  - Electronic journal of differential equations
PY  - 2010
VL  - 2010
UR  - http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a259/
LA  - en
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%A Petrović,  Nikola Z.
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%J Electronic journal of differential equations
%D 2010
%V 2010
%U http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a259/
%G en
%F EJDE_2010__2010__a259
Al Bastami,  Anas; Belić,  Milivoj R.; Petrović,  Nikola Z. Special solutions of the Riccati equation with applications to the Gross-Pitaevskii nonlinear PDE. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a259/