СОЛИТОННОЕ РЕШЕНИЕ СВЯЗАННОЙ СИСТЕМЫ НЕЛИНЕЙНЫХ УРАВНЕНИЙ КЛЕЙНА–ГОРДОНА НА МЕТРИЧЕСКИХ ГРАФАХ
DOI:
https://doi.org/10.56143/ujmcs.v2i2.6Ключевые слова:
связанная система нелинейных уравнений Клейна–Гордона; вершинные граничные условия; обобщенное правило Кирхгофа; безотражательное прохождение; солитонное решение; звездообразный граф.Аннотация
В данной работе рассматривается связанная система нелинейных уравнений Клейна–Гордона на простой сети, представляющей собой звездообразный граф. Доказана теорема о существовании солитонного решения рассматриваемой системы и его безотражательном прохождении через вершину графа. Основное внимание уделяется поведению волн в точке соединения, где накладываются условия непрерывности с весовыми коэффициентами и обобщённое правило Кирхгофа. С помощью аналитического подхода, основанного на склеивании солитонных решений на вершине графа, выводится правило суммы для нелинейностей связанной системы уравнений Клейна–Гордона на метрическом звездообразном графе. Это правило позволяет найти такие солитонные решения, которые проходят через вершину без отражения. Также показано, что для рассматриваемых солитонных решений на метрических звездообразных графах сохраняются функциональные выражения законов сохранения.
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