| 1. |
- Bona, J L, et al.
(author)
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Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
- 2005
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In: Annales de L'Institut Henri Poincaré. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449. ; 22:6, s. 783-797
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Journal article (peer-reviewed)abstract
- The generalized Korteweg-de Vries equation has the property that solutions with initial data that are analytic in a strip in the complex plane continue to be analytic in a strip as time progresses. Established here are algebraic lower bounds on the possible rate of decrease in time of the uniform radius of spatial analyticity for these equations. Previously known results featured exponentially decreasing bounds.
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| 2. |
- Bona, JL, et al.
(author)
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Singularity formation in the generalized Benjamin-Ono equation
- 2004
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In: Discrete and Continuous Dynamical Systems. Series A. - 1553-5231. ; 11:1, s. 27-45
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Journal article (peer-reviewed)abstract
- A Fourier-collocation scheme is used to approximate solutions to the generalized Benjamin-Ono equation u(t) + uP(Ux) - Hu(xx) = 0. The numerical simulation suggests that the equation features smooth solutions that become unbounded in finite time.
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| 3. |
- Craig, W, et al.
(author)
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A new model for large amplitude long internal waves
- 2004
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In: Comptes Rendus. Mecanique. - : Elsevier BV. - 1873-7234 .- 1631-0721. ; 332:7, s. 525-530
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Journal article (peer-reviewed)abstract
- We derive a new model for the description of large amplitude internal waves in a two-fluid system. The displacement of the interface between the two fluids is assumed to be of small slope, but no smallness assumption is made on the wave amplitude. The derivation of the model is based on the perturbation theory for Hamiltonian systems. In the case of a single fluid layer, the model reduces to the classical shallow water regime for surface water waves. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.
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| 4. |
- Ehrnström, Mats, et al.
(author)
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Traveling waves for the Whitham equation
- 2009
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In: Differential and Integral Equations. - 0893-4983. ; 22:11-12, s. 1193-1210
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Journal article (other academic/artistic)abstract
- The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves on finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities approach the limiting long-wave speed c0, and the waves approach a solitary wave. It is also shown that there can be no solitary waves with velocities much greater than c0. Finally, numerical approximations of some periodic traveling waves are presented.
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| 5. |
- Gurjic, Z, et al.
(author)
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The derivative nonlinear Schrodinger equation in analytic classes
- 2003
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In: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 10:Suppl. 1, s. 62-71
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Journal article (peer-reviewed)abstract
- The derivative nonlinear Schrodinger equation is shown to be locally well-posed in a class of functions analytic on a strip around the real axis. The main feature of the result is that the width of the strip does not shrink in time. To overcome the derivative loss, Kato-type smoothing results and space-time estimates are used.
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| 6. |
- Jiang, He, et al.
(author)
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Functional analysis of a gene-edited mouse model to gain insights into the disease mechanisms of a titin missense variant
- 2021
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In: Basic Research in Cardiology. - : Springer. - 0300-8428 .- 1435-1803. ; 116
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Journal article (peer-reviewed)abstract
- Titin truncating variants are a well-established cause of cardiomyopathy; however, the role of titin missense variants is less well understood. Here we describe the generation of a mouse model to investigate the underlying disease mechanism of a previously reported titin A178D missense variant identified in a family with non-compaction and dilated cardiomyopathy. Heterozygous and homozygous mice carrying the titin A178D missense variant were characterised in vivo by echocardiography. Heterozygous mice had no detectable phenotype at any time point investigated (up to 1 year). By contrast, homozygous mice developed dilated cardiomyopathy from 3 months. Chronic adrenergic stimulation aggravated the phenotype. Targeted transcript profiling revealed induction of the foetal gene programme and hypertrophic signalling pathways in homozygous mice, and these were confirmed at the protein level. Unsupervised proteomics identified downregulation of telethonin and four-and-a-half LIM domain 2, as well as the upregulation of heat shock proteins and myeloid leukaemia factor 1. Loss of telethonin from the cardiac Z-disc was accompanied by proteasomal degradation; however, unfolded telethonin accumulated in the cytoplasm, leading to a proteo-toxic response in the mice.We show that the titin A178D missense variant is pathogenic in homozygous mice, resulting in cardiomyopathy. We also provide evidence of the disease mechanism: because the titin A178D variant abolishes binding of telethonin, this leads to its abnormal cytoplasmic accumulation. Subsequent degradation of telethonin by the proteasome results in proteasomal overload, and activation of a proteo-toxic response. The latter appears to be a driving factor for the cardiomyopathy observed in the mouse model.
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| 7. |
- Kalisch, Henrik, et al.
(author)
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A numerical study of nonlinear dispersive wave models with SpecTraVVave
- 2017
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In: Electronic Journal of Differential Equations. - 1550-6150 .- 1072-6691. ; , s. 1-23
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Journal article (peer-reviewed)abstract
- In nonlinear dispersive evolution equations, the competing effects of nonlinearity and dispersion make a number of interesting phenomena possible. In the current work, the focus is on the numerical approximation of traveling-wave solutions of such equations. We describe our efforts to write a dedicated Python code which is able to compute traveling-wave solutions of nonlinear dispersive equations in a very general form. The Spec TraVVave code uses a continuation method coupled with a spectral projection to compute approximations of steady symmetric solutions of this equation. The code is used in a number of situations to gain an understanding of traveling-wave solutions. The first case is the Whitham equation, where numerical evidence points to the conclusion that the main bifurcation branch features three distinct points of interest, namely a turning point, a point of stability inversion, and a terminal point which corresponds to a cusped wave. The second case is the so-called modified Benjamin-Ono equation where the interaction of two solitary waves is investigated. It is found that two solitary waves may interact in such a way that the smaller wave is annihilated. The third case concerns the Benjamin equation which features two competing dispersive operators. In this case, it is found that bifurcation curves of periodic traveling-wave solutions may cross and connect high up on the branch in the nonlinear regime.
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| 8. |
- Kalisch, Henrik
(author)
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A uniqueness result for periodic traveling waves in water of finite depth
- 2004
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In: Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier BV. - 0362-546X. ; 58:7-8, s. 779-785
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Journal article (peer-reviewed)abstract
- It is shown that in water of finite depth, the surface profile eta of a periodic traveling wave uniquely determines the corresponding flow in the body of the fluid. This holds for rotational flow as long as the vorticity function gamma(psi) satisfies the condition gamma'(psi) max(xis an element ofR) eta(2)(x) < pi(2). This condition is also shown to be sharp.
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| 9. |
- Kalisch, Henrik, et al.
(author)
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Numerical study of traveling-wave solutions for the Camassa-Holm equation
- 2005
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In: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 25:2, s. 287-298
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Journal article (peer-reviewed)abstract
- We explore numerically different aspects of periodic traveling-wave solutions of the Camassa-Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied.
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| 10. |
- Kalisch, Henrik
(author)
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Periodic traveling water waves with isobaric streamlines
- 2004
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In: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 11:4, s. 461-471
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Journal article (peer-reviewed)abstract
- It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case of infinite depth, there is only one such solution, which is due to Gerstner.
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