Zobrazeno 1 - 10
of 481 981
pro vyhledávání: '"Benjamin P"'
Autor:
Aitzhan, Sultan, Ambrose, David M.
We consider the Benjamin-Ono equation in the spatially quasiperiodic setting. We establish local well-posedness of the initial value problem with initial data in quasiperiodic Sobolev spaces. This requires developing some of the fundamental propertie
Externí odkaz:
http://arxiv.org/abs/2412.12457
Autor:
Avramenko, Olga, Naradovyi, Volodymyr
The propagation of internal waves in a hydrodynamic system comprising a solid bottom and an upper half-space is investigated. The study is conducted within the framework of a nonlinear low-dimensional model incorporating surface tension on an interfa
Externí odkaz:
http://arxiv.org/abs/2411.15168
We prove the asymptotic stability of the high speed solitary waves to the Benjamin equation. This is done by establishing a Liouville property for the nonlinear evolution of the Benjamin equation around these solitary waves. To do this, inspired by K
Externí odkaz:
http://arxiv.org/abs/2410.17846
The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in $L^2(\mathbb{R})$ is obtained explicitly for generic rational initial data $u_0$. An explicit asymptotic wave profile $u^\mathr
Externí odkaz:
http://arxiv.org/abs/2410.17405
In the seminal work of Benjamin,\cite{Ben} in the late 70's, he has derived the ubiquitous Benjamin model, which is a reduced model in the theory of water waves. Notably, it contains two parameters in its dispersion part and under some special circum
Externí odkaz:
http://arxiv.org/abs/2408.16715
We examine the solution of the Benjamin-Ono Cauchy problem for rational initial data in three types of double-scaling limits in which the dispersion tends to zero while simultaneously the independent variables either approach a point on one of the tw
Externí odkaz:
http://arxiv.org/abs/2410.21581
For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families can be join
Externí odkaz:
http://arxiv.org/abs/2410.17416
We consider the $k$-dispersion generalized Benjamin-Ono ($k$-DGBO) equations. For nonlinearities with power $k \geq 4$, we establish local and global well-posedness results for the associated initial value problem (IVP) in both the critical and subcr
Externí odkaz:
http://arxiv.org/abs/2410.17217
We show that the initial-value problem for the Benjamin-Ono equation on $\mathbb{R}$ with $L^2(\mathbb{R})$ rational initial data with only simple poles can be solved in closed form via a determinant formula involving contour integrals. The dimension
Externí odkaz:
http://arxiv.org/abs/2410.14870
Autor:
Shin, Wangseok
We consider the periodic dispersion generalized Benjamin-Ono equations with polynomial nonlinearity. We establish the nonlinear smoothing properties of these equations, according to which the difference between the solution and the linear evolution i
Externí odkaz:
http://arxiv.org/abs/2410.13151