• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Differential and integral equations >THE CAUCHY PROBLEM AND STABILITY OF SOLITARYWAVES FOR A 2D BOUSSINESQ-KDV TYPE SYSTEM
【24h】

THE CAUCHY PROBLEM AND STABILITY OF SOLITARYWAVES FOR A 2D BOUSSINESQ-KDV TYPE SYSTEM

机译：二维BOUSSINESQ-KDV型系统孤波的Cauchey问题和稳定性

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We address the well posedness of the Cauchy problem and the st bility of solitary waves for a Boussinesq system in R~(1+2). We ex-ploit the fact that this 2D system has a "KdV" structure in the sense that it takes the form U_t = A_0U + A(U)U, where A_0 is a third-order linear operator and the entries of the operator A(U)(U) are linear combinations of products of powers of components of U with its order one spatial derivatives, as in the well-known 1D-KdV model. Using this "2D-KdV" structure, we establish existence and uniqueness for the Cauchy problem associated with the Boussinesq type system by following Kato's approach for the generalized KdV equation. By a variational argument, we obtain global well posedness in time for small initial data. We prove orbital stability of solitary waves directly, by using a variational ap-proach involving the characterization of the ground state solutions, as is done for some 2-D models.
机译：我们讨论了柯西问题的适定性和R〜（1 + 2）中Boussinesq系统的孤波的稳定性。我们从这个二维系统具有“ KdV”结构这一事实着手，它的形式为U_t = A_0U + A（U）U，其中A_0是三阶线性算子，而算子A的项与众所周知的1D-KdV模型一样，（U）（U）是U的分量幂及其一阶空间导数乘积的线性组合。使用这种“ 2D-KdV”结构，我们遵循加藤对广义KdV方程的方法，建立了与Boussinesq型系统相关的柯西问题的存在性和唯一性。通过变分论证，我们可以及时获得较小初始数据的全局适定性。我们通过使用涉及基态解特征的变分方法，直接证明了孤波的轨道稳定性，就像对某些二维模型所做的那样。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号