Special solutions of the riccati equation with applications to the gross-pitaevskii nonlinear PDE

Anas Al Bastami, Milivoj R. Belić, Nikola Z. Petrović

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

A method for finding solutions of the Riccati differential equation y'= P(x) + Q(x)y + R(x)y2 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.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalElectronic Journal of Differential Equations
Volume2010
Publication statusPublished - 2010
Externally publishedYes

Keywords

  • Chirp function
  • Riccati equation
  • Solutions to gross-pitaevskii equation

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