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Meromorphic solutions of autonomous ordinary differential equations without the finiteness property
Journal of Mathematical Analysis and Applications. 2022. Vol. 516. No. 2. Article 126516.
We consider the problem of finding meromorphic solutions of autonomous algebraic ordinary differential equations possessing an infinite number of local solutions given by Laurent series in neighborhoods of poles. We present an algebraic-geometric method for finding all meromorphic solutions that are elliptic or rational in the exponential function. As an example, we classify such families of meromorphic solutions for fourth-order ordinary differential equations arising via integrating once traveling-wave reductions of the generalized Rosenau–Korteweg–de Vries equation and the fifth-order Korteweg–de Vries–Burgers equation. Solutions important from a physical point of view are presented.
Keywords: Puiseux seriesmeromorphic solutionsМероморфные решенияAlgebraic invariantsGeneralized Rosenau–Korteweg–de Vries equationFifth-order Korteweg–de Vries–Burgers equationряды Пюизёалгебраические инвариантыобобщенное уравнение Розена - Кортевега - де Вризауравнение Кортевега - де Вриза - Бюргерса пятого порядка
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In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
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