Nonradial Solutions of a Nonlinear Elliptic Equation
(2017) In Bachelor's Theses in Mathematical Sciences MATK01 20162Mathematics (Faculty of Sciences)
- Abstract
- We consider the partial differential equation ∆u + f(u) = 0 in two dimensions,where f is a nonlinear function of u. Under certain assumptions on f we show that the equation has non-radial C² solutions with u(x) → 0 as |x| → 0 with an arbitrary number of zeros on each axis. The equation has applications in Bose-Einstein condensation and water waves among other fields. We also look at numerical solutions in the special case f(u) = |u|²u − u.
- Popular Abstract (Swedish)
- I detta arbete studerar vi en partiell differentialekvation som bland annat används som en modell för vattenvågor och Bose-Einstein-kondensat. Vi undersöker lösningar som är icke-radiella och går mot noll i oändligheten. Genom att göra en speciell ansats reducerar vi ekvationen till en ordinär differentialekvation. Vi visar att denna ekvation har lösningar med godtyckligt antal nollställen. Vi undersöker även numeriska lösningar.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/8904338
- author
- Andersson, Sebastian LU
- supervisor
-
- Erik Wahlén LU
- organization
- course
- MATK01 20162
- year
- 2017
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFMA-4057-2017
- ISSN
- 1654-6229
- other publication id
- 2017:K3
- language
- English
- id
- 8904338
- date added to LUP
- 2017-03-28 14:34:17
- date last changed
- 2017-03-28 14:34:17
@misc{8904338, abstract = {{We consider the partial differential equation ∆u + f(u) = 0 in two dimensions,where f is a nonlinear function of u. Under certain assumptions on f we show that the equation has non-radial C² solutions with u(x) → 0 as |x| → 0 with an arbitrary number of zeros on each axis. The equation has applications in Bose-Einstein condensation and water waves among other fields. We also look at numerical solutions in the special case f(u) = |u|²u − u.}}, author = {{Andersson, Sebastian}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{Nonradial Solutions of a Nonlinear Elliptic Equation}}, year = {{2017}}, }