# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Nonradial Solutions of a Nonlinear Elliptic Equation

(2017) In Bachelor's Theses in Mathematical Sciences MATK01 20162
Mathematics (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.
author
supervisor
organization
course
MATK01 20162
year
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
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.},
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},
}

```