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Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, we will first review recent progress in singu...
We consider the reactive Boussinesq equations in a slanted cylinder, with zero stress boundary conditions and arbitrary Rayleigh number. We show that the equations have non-planar traveling front solu...
We consider systems of reactive Boussinesq equations in two dimensional strips that are not aligned with gravity s direction. We prove that for any width of such strips and for arbitrary Rayleigh and ...
We investigate the qualitative behavior of solutions of a Burgers-Boussinesq system – a reaction-diffusion equation coupled via gravity to a Burgers equation – by a combination of numerical, asymptoti...
We consider systems of reactive Boussinesq equations in two dimensional strips that are not aligned with gravity's direction. We prove that for any width of such strips and for arbitrary Rayleigh and ...
We give an example of a well posed, nite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce nite time sing...
本文借助于Bell多项式研究经典Boussinesq方程,将其转换成Hirota双线性形式,构造了带参数的Bäcklund变换,进而重新导出了其Lax表示.
α和β都是正常数.许多逼近模型都能从此系统中被推导出,比如Boussinesq系统和两分量Camassa-Holm系统等.本文利用平面动力系统方法研究它的行波解及相图,得到了孤立波解,广义扭波解,广义反扭波解,紧孤立波解和周期波解,并给出了这些解的数值模拟.
本文研究了耦合Schrodinger-Boussinesq方程组的孤立波和周期波解,在给定参数条件下,利用动力系统理论,获得了该方程组孤立波与周期波解的精确参数表达式,并推广了已有文献的相应结果。
Abstract: This work studies the stability of solitary waves of a class of sixth-order Boussinesq equations.
This work studies the local well-posedness of the initial-value problem for the nonlinear sixth-order Boussinesq equation utt = uxx + uxxxx + uxxxxxx + (u2)xx, where = ±1. We prove local well-posed...
We consider quasilinear, multi-variable, constant coefficient, lattice equations defined on the edges of the elementary square of the lattice, modeled after the lattice modified Boussinesq (lmBSQ) eq...
A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference disc...
Based on the homotopy perturbation method (HPM) and Padé approximants (PA), explicit approximate and exact solutions are obtained for cubic Boussinesq equations. HPM is used for analytic treatment to ...
We prove the local in time existence and a blow up criterion of solution in the H¨older spaces for the inviscid Boussinesq system in RN,N ≥ 2, under the assumptions that the initial values θ0, u0 ∈ C...

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