Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Bernard Deconinck"'
Publikováno v:
Fluids, Vol 6, Iss 4, p 136 (2021)
We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq–Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on the real
Externí odkaz:
https://doaj.org/article/658e3505ae6149b4ab3bdc13551fa368
Autor:
Jorge Cisneros, Bernard Deconinck
Publikováno v:
Quarterly of Applied Mathematics. 80:739-786
We study a semidiscrete analogue of the Unified Transform Method introduced by A. S. Fokas, to solve initial-boundary-value problems for linear evolution partial differential equations with constant coefficients on the finite interval $x \in (0,L)$.
Autor:
John D. Carter, Bernard Deconinck
Publikováno v:
Studies in Applied Mathematics. 147:1199-1208
Autor:
Matthew Farkas, Bernard Deconinck
We consider the heat equation with spatially variable thermal conductivity and homogeneous Dirichlet boundary conditions. Using the Method of Fokas or Unified Transform Method, we derive solution representations as the limit of solutions of constant-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6cad2cf7742117bf773f68798c812287
http://arxiv.org/abs/2208.01764
http://arxiv.org/abs/2208.01764
Autor:
Ryan P. Creedon, Bernard Deconinck
We investigate the Benjamin-Feir (or modulational) instability of Stokes waves, i.e., small-amplitude, one-dimensional periodic gravity waves of permanent form and constant velocity, in water of finite and infinite depth. We develop a perturbation me
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b3d92928695279a818657eec5e5ab697
http://arxiv.org/abs/2206.01817
http://arxiv.org/abs/2206.01817
Publikováno v:
SIAM Journal on Applied Dynamical Systems. 20:1571-1595
We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of the Kawahara equation. These solutions exhibit high-frequency instabilities when subject to bounded perturbations on the whole real line. We introduce a forma
Autor:
Bernard Deconinck, Jeremy Upsal
Publikováno v:
SIAM Journal on Mathematical Analysis. 52:1-41
We examine the stability of the elliptic solutions of the focusing nonlinear Schrodinger equation (NLS) with respect to subharmonic perturbations. Using the integrability of NLS, we discuss the spe...
Publikováno v:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 477
We implement the numerical unified transform method to solve the nonlinear Schrödinger equation on the half-line. For the so-called linearizable boundary conditions, the method solves the half-line problems with comparable complexity as the numerica
Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes waves, i.e.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5c0d5abac53da46cdf2302f3576d15a
http://arxiv.org/abs/2107.11489
http://arxiv.org/abs/2107.11489
Autor:
Wen-Rong Sun, Bernard Deconinck
Publikováno v:
Journal of Nonlinear Science. 31
Using the integrability of the sinh-Gordon equation, we demonstrate the spectral stability of its elliptic solutions. With the first three conserved quantities of the sinh-Gordon equation, we construct a Lyapunov functional. By using such Lyapunov fu