Article
Ufa Mathematical Journal
Volume 3, Number 4, pp. 141-147
Integrating the Korteweg-de Vries equation with a especial free term in the class of periodic functions
Yakhshimuratov A.B.
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In this work considered Cauchy problem for the Korteweg-de Vries equation with a free term which is not depend from the spatial variable, in the class of periodic functions. Is obtained a law of evolution of spectral data Sturm-Liouville’s operator which potential is the solution of posed problem. The spectrum of this operator moves along the axis while preserving its initial structure is shown. Is shown method of solving posed Cauchy problem. Is obtained corollaries about period and analyticity of solution with respect spatial variable, depending on the period and analyticity of initial function.