Results 41 to 50 of about 168,001 (284)

Traveling wave solutions to the Allen–Cahn equation

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2022
For the Allen–Cahn equation, it is well known that there is a monotone standing wave joining the balanced wells of the potential. In this paper we study the existence of traveling wave solutions for the Allen–Cahn equation on an infinite channel. Such traveling wave solutions possess a large number of oscillations and they are obtained with the aid of ...
Chen, Chao-Nien, Coti Zelati, Vittorio
openaire   +4 more sources

Five‐Year Disease Progression in Synuclein Seeding Positive Sporadic Parkinson's Disease

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective To provide a comprehensive description of disease progression in synuclein seeding assay (SAA) positive sporadic Parkinson Disease participants, using Neuronal Synuclein Disease integrated biological and functional impairment staging framework.
Paulina Gonzalez‐Latapi, Caroline Gochanour, Seung Ho Choi, Hyunkeun Cho, Chelsea Caspell‐Garcia, Christopher Coffey, Michael Brumm, David‐Erick Lafontant, Yuge Xiao, Thomas Tropea, John Seibyl, Caroline Tanner, Charles S. Venuto, Karl Kieburtz, Lana M. Chahine, Kathleen L. Poston, Andrew Siderowf, Kenneth Marek, Tanya Simuni, The Parkinson's Progression Markers Initiative   +19 more
wiley   +1 more source

Extended Tanh-Function Method and Its Applications in Nonlocal Complex mKdV Equations

Mathematics, 2022
In order to construct the multiple traveling wave solutions of the nonlocal modified Korteweg de Vires (mKdV) equation, the modified tanh-function approach for local soliton equations is extended to a nonlocal complex mKdV equation.
Xiaodong Wang, Jianping Wu, Yazi Wang, Can Chen   +3 more
doaj   +1 more source

Brunet-Derrida particle systems, free boundary problems and Wiener-Hopf equations

, 2012
We consider a branching-selection system in $\mathbb {R}$ with $N$ particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. We show that, as $N\to\infty$, the
Durrett, Rick, Remenik, Daniel
core   +1 more source

Ketogenic Diet as an Epigenetic Therapy in SETD1B‐Related Epilepsy

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Histone lysine methyltransferases such as SETD1B regulate chromatin structure and gene transcription. Ketone bodies, including butyrate, act as histone deacetylase inhibitors. We report a 4‐year‐old boy with SETD1B‐related absence epilepsy, refractory to conventional medications, who achieved sustained > 90% seizure reduction on the Modified ...
Erica Tsang, Brian S. Gloss, Jessica P. Hayes, Andrew J. A. Holland, Manoj P. Menezes, Joceline A. Branson, Shekeeb S. Mohammad, Jingya J. Yan, Shrujna Patel, Velda X. Han, Russell C. Dale   +10 more
wiley   +1 more source

New applications of the two variable (G′/G, 1/G)-expansion method for closed form traveling wave solutions of integro-differential equations

Journal of Ocean Engineering and Science, 2019
Most fundamental themes in mathematical physics and modern engineering are investigated by the closed form traveling wave solutions of nonlinear evolution equations.
M. Mamun Miah, H.M. Shahadat Ali, M. Ali Akbar, Aly R. Seadawy   +3 more
doaj   +1 more source

Global well-posedness for the KP-I equation on the background of a non localized solution

, 2006
We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g.
A.A. Zaitsev, A.S. Fokas, A.S. Fokas, C. Gallo, C. Kenig, C. Kenig, C. Kenig, C.E. Kenig, C.E. Kenig, H. Koch, H. Takaoka, H. Takaoka, J. Bourgain, J. C. Saut, J. Kato, J.-L. Lions, J.C. Alexander, J.C. Saut, L. Molinet, L. Molinet, L. Molinet, L. Molinet, M. Haragus, M. Tajeri, M.D. Groves, M.Jr. Schwarz, M.V. Wickerhauser, N. Burq, N. Tzvetkov, N. Tzvetkov, N.C. Freeman, O. Besov, P. Isaza, R.J. Iório Jr, T. Kato, V. Zakharov, V.E. Zakharov, X. Zhou   +37 more
core   +3 more sources

Aquaporin‐4 in Narcolepsy Type 1: Investigation of Perivascular Fluid Movement in Sleep Disorders

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Narcolepsy type 1 (NT1) is caused by the loss of hypocretin‐1 leading to excessive daytime sleepiness and cataplexy. Additionally, disrupted nighttime sleep has become an increasingly recognized feature of NT1. As the glymphatic fluid movement has been linked to sleep architecture, we investigated cerebrospinal fluid (CSF) Aquaporin‐4 (AQP4 ...
Jonas Ranke, Petra Steinacker, Steffen Halbgebauer, Patrick Oeckl, Geert Mayer, Markus Otto   +5 more
wiley   +1 more source

Global bifurcation for the Whitham equation

, 2013
We prove the existence of a global bifurcation branch of $2\pi$-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some ...
Ehrnstrom, Mats, Kalisch, Henrik
core   +1 more source

Travelling wave solutions on an axisymmetric ferrofluid jet [PDF]

Journal of Fluid Mechanics, 2019
We consider a potential flow model of axisymmetric waves travelling on a ferrofluid jet. The ferrofluid coats a copper wire, through which an electric current is run. The induced azimuthal magnetic field magnetises the ferrofluid, which in turn stabilises the well known Plateau–Rayleigh instability seen in axisymmetric capillary jets.
A. Doak, J.-M. Vanden-Broeck
openaire   +2 more sources