论文标题
n波相互作用问题的逆散射变换在两个空间维度中具有分散术语
Inverse scattering transform for N-wave interaction problem with a dispersive term in two spatial dimensions
论文作者
论文摘要
在这项工作中，我们引入了一个分散n（= 2n） - 波相互作用问题，涉及两个空间维度和一个时间维度的n速度。展示了问题的确切解决方案。这是对N波相互作用问题和矩阵Davey-Stewartson方程的概括，具有2+1个维度，该方程检查了短波和长波之间的Benney-type相互作用模型。因此，与Manakov系统的二维类似物的解，Gelfand-Levitan-Marchenko（GLM）型或所谓的倒置样式相关联，构建了方程。结果表明，退化内核的存在读取了分散n波相互作用问题的精确词素样解决方案。我们还提到了库奇问题的独特解决方案在任意时间间隔中用于小型初始数据。
In this work, we introduce a dispersive N(=2n)-wave interaction problem involving n velocities in two spatial dimensions and one temporal dimension. Exact solutions of the problem are exhibited. This is a generalization of the N-wave interaction problem and matrix Davey-Stewartson equation with 2+1 dimensions that examines the Benney-type model of interactions between short and long waves. Accordingly, associated with the solutions of two dimensional analog of the Manakov system, a Gelfand-Levitan-Marchenko (GLM)-type, or so-called inversion-like, equation is constructed. It is shown that the presence of the degenerate kernel reads exact soliton-like solutions of the dispersive N-wave interaction problem.We also mention the unique solution of the Cauchy problem on an arbitrary time interval for small initial data.
