Electron. J. Diff. Equ., Vol. 2010(2010), No. 66, pp. 1-10.

Special solutions of the Riccati equation with applications to the Gross-Pitaevskii nonlinear PDE

Anas Al Bastami, Milivoj R. Belic, Nikola Z. Petrovic

Abstract:
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.

Submitted April 6, 2010. Published May 8, 2010.
Math Subject Classifications: 34A34, 34A05.
Key Words: Riccati equation; solutions to Gross-Pitaevskii equation; chirp function.

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Anas Al Bastami
Science Program, Texas A&M University at Qatar,
P.O. Box 23874 Doha, Qatar
email: anas.al_bastami@qatar.tamu.edu
Milivoj R. Belic
Science Program, Texas A&M University at Qatar,
P.O. Box 23874 Doha, Qatar
email: milivoj.belic@qatar.tamu.edu
Nikola Z. Petrovic
Science Program, Texas A&M University at Qatar,
P.O. Box 23874 Doha, Qatar
email: nikola.petrovic@qatar.tamu.edu

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