发表机构
Institute of Mathematics, Ufa Federal Research Centre, Russian Academy of Sciences（俄罗斯科学院乌法联邦研究中心数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明两类Bäcklund变换保持Darboux可积性，并用于检验方程列表完备性，由此构造了一个由三个二元任意函数参数化的新Darboux可积方程族。
AI 中文摘要
本文研究标量双曲型偏微分方程的两种Bäcklund变换。我们证明这两种变换都将Darboux可积方程的解映射为（一般而言）另一个同样Darboux可积方程的解。后一事实可用于粗略检验Darboux可积方程列表的完备性。为说明这一点，我们将上述变换应用于一个众所周知的Darboux可积方程列表中的若干方程，结果得到一个不在该列表中但目前已为人所知的Darboux可积方程。作为最后一个方程的推广，我们构造了一个由三个任意函数参数化的Darboux可积方程族，每个函数依赖于两个自变量。该方程族可能是新的。
英文摘要
This paper deals with two kinds of Bäcklund transformations for scalar hyperbolic partial differential equations. We prove that both these types of transformations map solutions of a Darboux integrable equation into solutions of, generally speaking, another but also Darboux integrable equation. The latter fact can be used to roughly check the completeness of a list of Darboux integrable equations. To illustrate this, we apply the above transformations to several equations from a well-known list of Darboux integrable equations and, as a result, obtain a Darboux integrable equation which is absent in this list, but is already known at present. As a generalization of the last equation, we construct a family of Darboux integrable equations that is parametrized by three arbitrary functions, each of which depends on two arguments. This family is probably new.
Comments12 pages
Journal refLobachevskii J. Math., 44:5 (2023), 1929-1937
