Local well-posedness for dispersion generalized Benjamin-Ono equations [PDF]
arXiv, 2002 In this paper we study local well-posedness in the energy space for a family of dispersive equations that can be seen as dispersive ``interpolations'' between the KdV and the Benjamin-Ono equation.
arxiv
A variety of soliton solutions for the fractional Wazwaz-Benjamin-Bona-Mahony equations
Results in Physics, 2019 In the present paper, the new three-dimensional modified Benjamin-Bona-Mahony equations recently introduced are analyzed with the introduction of the spatial and temporal fractional order derivatives using conformable fractional derivative.
Aly R. Seadawy +2 more
doaj
Coupling for some partial differential equations driven by white noise [PDF]
arXiv, 2004 We prove, using coupling arguments, exponential convergence to equilibrium for reaction--diffusion and Burgers equations driven by space-time white noise. We use a coupling by reflection.
arxiv
Results in Physics, 2017 The higher order nonlinear Schrödinger (NLS) equation describes ultra-short pluse propagation in optical fibres. By using the amplitude ansatz method, we derive the exact bright, dark and bright-dark solitary wave soliton solutions of the generalized ...
Aly R. Seadawy, Dianchen Lu
doaj
A priori estimates for solutions of a nonlinear dispersive equation [PDF]
arXiv, 2005 This paper has been withdrawn by the author due to a crucial error.
arxiv
Global regular solutions for the 3D Zakharov-Kuznetsov equation posed on a bounded domain [PDF]
, 2014 An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on bounded domains is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the $H^2$-norm for small initial data are proven.
arxiv +1 more source
Well-posedness in H^1 for the (generalized) Benjamin-Ono equation on the circle [PDF]
arXiv, 2006 We prove the local well posedness of the Benjamin-Ono equation and the generalized Benjamin-Ono equation in $ H^1(\T) $. This leads to a global well-posedness result in $ H^1(\T)$ for the Benjamin-Ono equation.
arxiv
On generating functions in additive number theory, II: lower-order terms and applications to PDEs. [PDF]
Math Ann, 2021 Brandes J +4 more
europepmc +1 more source
On the Cauchy problem for higher-order nonlinear dispersive equations [PDF]
arXiv, 2007 We study a class of higher-order KdV equations. We show that the associated initial value problem is well posed in weighted Besov and Sobolev spaces for small initial data. We also prove ill-posedness results when in H^s(\R), for any real s.
arxiv
A scalar Riemann-Hilbert problem on the torus: applications to the KdV equation. [PDF]
Anal Math Phys, 2022 Piorkowski M, Teschl G.
europepmc +1 more source