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Open Problems

To celebrate Nonlinearity's 20th anniversary, a series of Open Problems articles was published in issues throughout 2008. These short, commissioned articles present personal selections of interesting and/or important problems and challenges, large and small, from leaders in the field. Our hope is that these articles will contribute to setting the agenda for future research. We are pleased to make these Open Problems freely available online until the end of 2010.

To order your personal copy of the reprint collection containing all 30 Open Problems for just GBP £15/USD $28.50 per copy (including postage and packaging), please download the order form.

We hope you enjoy reading these articles as much as we have. We welcome your feedback on these articles - any comments should be sent to the Nonlinearity publishing team via non@iop.org

Kate Watt
Publisher, Nonlinearity

EDITORIAL
 
Nonlinearity is 20 years old in 2008!
J P Keating and A I Neishtadt
Nonlinearity 21 No 1 (January 2008)
Full text Full text:  Acrobat PDF (103 KB)
 

OPEN PROBLEMS
 
Turbulence transition in pipe flow: some open questions
Bruno Eckhardt
Nonlinearity 21 No 1 (January 2008) T1-T11
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (644 KB)
 
Relative volume of Kolmogorov–Arnold–Moser tori and uniform distribution, stickiness and nonstickiness in Hamiltonian systems
Leonid A Bunimovich
Nonlinearity 21 No 2 (February 2008) T13-T17
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (83.3 KB)
 
Three quantum obsessions
M V Berry
Nonlinearity 21 No 2 (February 2008) T19-T26
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (105 KB)
 
Convergence, nonconvergence and adiabatic transitions in fully coupled averaging
Yuri Kifer
Nonlinearity 21 No 3 (March 2008) T27-T32
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (99.7 KB)
 
Orbits with historic behaviour, or non-existence of averages
Floris Takens
Nonlinearity 21 No 3 (March 2008) T33-T36
Abstract  |  References Full text:  Acrobat PDF (69.3 KB)
 
Open questions leading to a global perspective in dynamics
J Palis
Nonlinearity 21 No 4 (April 2008) T37-T43
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (96.1 KB)
 
Spatially localized structures in dissipative systems: open problems
E Knobloch
Nonlinearity 21 No 4 (April 2008) T45-T60
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (659 KB)
 
Wave-breaking and generic singularities of nonlinear hyperbolic equations
Yves Pomeau, Martine Le Berre, Philippe Guyenne and Stephan Grilli
Nonlinearity 21 No 5 (May 2008) T61-T79
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (363 KB)
 
Linear response despite critical points
Viviane Baladi
Nonlinearity 21 No 6 (June 2008) T81-T90
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (169 KB)
 
Modelling DNA at the mesoscale: a challenge for nonlinear science?
Michel Peyrard, Santiago Cuesta-López and Guillaume James
Nonlinearity 21 No 6 (June 2008) T91-T100
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (727 KB)
 
Some open problems in real and complex dynamical systems
Yu Ilyashenko
Nonlinearity 21 No 7 (July 2008) T101-T107
Abstract  |  References Full text:  Acrobat PDF (94.4 KB)
 
Orbits' statistics in chaotic dynamical systems
V Arnold
Nonlinearity 21 No 7 (July 2008) T109-T112
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (61.9 KB)
 
Some open questions in 'wave chaos'
Stéphane Nonnenmacher
Nonlinearity 21 No 8 (August 2008) T113-T121
Abstract  |  References Full text:  Acrobat PDF (123 KB)
 
The three-dimensional Euler equations: singular or non-singular?
J D Gibbon, M Bustamante and R M Kerr
Nonlinearity 21 No 8 (August 2008) T123-T129
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (117 KB)
 
Some nonlinear challenges in biology
Francesco Mosconi, Thomas Julou, Nicolas Desprat, Deepak Kumar Sinha, Jean-François Allemand, Vincent Croquette and David Bensimon
Nonlinearity 21 No 8 (August 2008) T131-T147
Abstract  |  References Full text:  Acrobat PDF (844 KB)
 
Several problems on dynamical systems and mechanics
V V Kozlov
Nonlinearity 21 No 9 (September 2008) T149-T155
Abstract  |  References Full text:  Acrobat PDF (81.5 KB)
 
Some problems in differential geometry and topology
S K Donaldson
Nonlinearity 21 No 9 (September 2008) T157-T164
Abstract  |  References Full text:  Acrobat PDF (92.3 KB)
 
Molecular simulation and related topics: some open mathematical problems
Eric Cancès, C Le Bris and P-L Lions
Nonlinearity 21 No 9 (September 2008) T165-T176
Abstract  |  References Full text:  Acrobat PDF (372 KB)
 
KAM tori: persistence and smoothness
Mikhail B Sevryuk
Nonlinearity 21 No 10 (October 2008) T177-T185
Abstract  |  References Full text:  Acrobat PDF (152 KB)
 
Some challenges in the theory of (semi)-dispersing billiards
Domokos Szász
Nonlinearity 21 No 10 (October 2008) T187-T193
Abstract  |  References Full text:  Acrobat PDF (104 KB)
 
Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations
J L Bona and A S Fokas
Nonlinearity 21 No 10 (October 2008) T195-T203
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (123 KB)
 
Geometric function theory: a modern view of a classical subject
Darren Crowdy
Nonlinearity 21 No 10 (October 2008) T205-T219
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (595 KB)
 
Solitons as elementary particles: a paradigm scrutinized
Nicholas S Manton
Nonlinearity 21 No 11 (November 2008) T221-T232
Abstract  |  References Full text:  Acrobat PDF (128 KB)
 
Some simple questions related to the Cr stability conjecture
Enrique R Pujals
Nonlinearity 21 No 11 (November 2008) T233-T237
Abstract  |  References Full text:  Acrobat PDF (74.5 KB)
 
Partial differential equation problems from simple to complex fluids
Peter Constantin
Nonlinearity 21 No 11 (November 2008) T239-T244
Abstract  |  References Full text:  Acrobat PDF (83.4 KB)
 
Chaotic phenomena in three settings: large, noisy and out of equilibrium
Lai-Sang Young
Nonlinearity 21 No 11 (November 2008) T245-T252
Abstract  |  References  |  Citing articles Full text:  Acrobat PDF (99.4 KB)
 
Two limit theorems
Ya G Sinai
Nonlinearity 21 No 12 (December 2008) T253-T254
Abstract  |  References Full text:  Acrobat PDF (44.8 KB)
 
A miscellany of basic issues on incompressible fluid equations
Koji Ohkitani
Nonlinearity 21 No 12 (December 2008) T255-T271
Abstract  |  References Full text:  Acrobat PDF (212 KB)
 
Nonlinearity in complexity science
R S MacKay
Nonlinearity 21 No 12 (December 2008) T273-T281
Abstract  |  References Full text:  Acrobat PDF (106 KB)
 
Partial differential equations and non-diffusive structures
A Stevens and J J L Velázquez
Nonlinearity 21 No 12 (December 2008) T283-T289
Abstract  |  References Full text:  Acrobat PDF (100 KB)
 
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