Holomorphic solutions of soliton equations

A. Domrin
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引用次数: 1

Abstract

We present a holomorphic version of the inverse scattering method for soliton equations of parabolic type in two-dimensional space-time. It enables one to construct examples of solutions holomorphic in both variables and study the properties of all such solutions. We show that every local holomorphic solution of any of these equations admits an analytic continuation to a globally meromorphic function of the spatial variable. We also discuss the role of the Riemann problem in the theory of integrable systems, solubility conditions for the Cauchy problem, the property of trivial monodromy for all solutions of the auxiliary linear system, and the Painlevé property for soliton equations.
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孤子方程的全纯解
给出了二维时空中抛物型孤子方程逆散射方法的全纯版本。它使我们能够构造两个变量全纯解的例子,并研究所有这些解的性质。我们证明了这些方程的每一个局部全纯解都允许对空间变量的全局亚纯函数的解析延拓。我们还讨论了黎曼问题在可积系统理论中的作用,柯西问题的溶解度条件,辅助线性系统所有解的平凡单调性质,以及孤子方程的painlevevl性质。
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来源期刊
Transactions of the Moscow Mathematical Society
Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)
自引率
0.00%
发文量
19
期刊介绍: This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.
期刊最新文献
On generalized Newton’s aerodynamic problem The asymptotic behaviour of cocycles over flows Holomorphic solutions of soliton equations Realizing integrable Hamiltonian systems by means of billiard books Letter to the Editors
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