ASYMPTOTICS OF THE SOLUTION OF THE CAUCHY PROBLEM FOR THE KORTEWEG-de VRIES EQUATION WITH INITIAL DATA OF STEP TYPE
ASYMPTOTICS OF THE SOLUTION OF THE CAUCHY PROBLEM FOR THE KORTEWEG-de VRIES EQUATION WITH INITIAL DATA OF STEP TYPE
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具有阶跃型初始数据的KORTEWEG-de Vries方程柯西问题解的渐近性
DOI：
10.1070/sm1976v028n02abeh001649
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
E. J. Hruslov
中科院分区：
文献类型：
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作者：
E. J. Hruslov
本文用反散射问题的方法求解了具有阶跃型初值的Korteweg-deVries方程的Cauchy问题。公式获得的散射数据相对于时间的转换，使它能够获得一个解决方案的问题，为任意的援助的线性积分方程的散射理论。在波前的一个邻域内研究了解的渐近性态。结果表明，在这个区域中的解决方案分裂成孤子，之间的距离增加，这些孤子的显式形式的推导。参考书目：12种。
The method of the inverse scattering problem is used to solve the Cauchy problem for the Korteweg-deVries equation with initial data of step type: , . Formulas are obtained for transforming the scattering data with respect to the time, making it possible to obtain a solution of the problem for arbitrary with the aid of linear integral equations of scattering theory. The asymptotic behavior of the solution as is investigated in a neighborhood of the wave front . It is shown that in this region the solution splits up into solitons, the distance between which increases as , and an explicit form for these solitons is derived. Bibliography: 12 titles.