论文标题
GKDV方程耦合系统的孤立波解决方案和全球适应性
Solitary wave solutions and global well-posedness for a coupled system of gKdV equations
论文作者
论文摘要
在这项工作中，我们考虑了与广义korteweg-de Vries方程的耦合系统相关的初始值问题。我们提出了Gagliardo-Nirenberg类型不平等的最佳常数与能源空间中全球解决方案存在的标准之间的关系。我们证明，这样的常数与具有最小质量的单位波解决方案的存在问题直接相关，即所谓的基态溶液。为了确保基础状态的存在，我们使用一种变分方法。
In this work we consider the initial-value problem associated with a coupled system of generalized Korteweg-de Vries equations. We present a relationship between the best constant for a Gagliardo-Nirenberg type inequality and a criterion for the existence of global solutions in the energy space. We prove that such a constant is directly related to the existence problem of solitary-wave solutions with minimal mass, the so called ground state solutions. To guarantee the existence of ground states we use a variational method.
