论文标题
通用BousSinesQ方程的解决方案的长期行为
Long time behavior of solutions to the generalized Boussinesq equation
论文作者
论文摘要
在本文中，我们研究了广义的Boussinesq方程，作为表面张力的水浪问题的模型。最初，我们研究了Sobolev空间内的初始价值问题，从而得出了解决方案是全局或经验爆炸的条件。随后，我们将分析扩展到贝塞尔电位和调制空间，确定解决方案的渐近行为。我们使用pohozaev型身份为某些参数建立了孤立波的不存在。此外，我们通过PETVIASHVILI迭代方法来数值生成广义Boussinesq方程的孤立波解。为了进一步研究溶液的时间演变，我们提出采用傅立叶伪谱数值方法。我们的调查扩展到差距间隔，理论上都没有建立全球存在和爆炸结果。我们发现我们的数值结果有效地填补了这些空白，并补充了理论发现。
In this paper, we study the generalized Boussinesq equation as a model for the water wave problem with surface tension. Initially, we investigate the initial value problem within Sobolev spaces, deriving conditions under which solutions are either global or experience blow-up in time. Subsequently, we extend our analysis to Bessel potential and modulation spaces, determining the asymptotic behavior of solutions. We establish the non-existence of solitary waves for certain parameters using Pohozaev-type identities. Additionally, we numerically generate solitary wave solutions of the generalized Boussinesq equation through the Petviashvili iteration method. To further examine the time evolution of solutions, we propose employing the Fourier pseudo-spectral numerical method. Our investigation extends to the gap interval, where neither global existence nor blow-up results have been theoretically established. We find that our numerical results effectively fill these gaps, supplementing the theoretical findings.
