SOLITON SOLUTION OF THE COUPLED NONLINEAR KLEIN-GORDON EQUATIONS ON METRIC GRAPHS
DOI:
https://doi.org/10.56143/ujmcs.v2i2.6Keywords:
связанная система нелинейных уравнений Клейна–Гордона; вершинные граничные условия; обобщенное правило Кирхгофа; безотражательное прохождение; солитонное решение; звездообразный граф.Abstract
In this paper, we study the coupled nonlinear Klein-Gordon equations on a simple network in the form of a star graph. A theorem is proved on the existence of a soliton solution of the equation and reflectionless transmission through the vertices of the graph. We focus on how waves behave at the junction, where weighted continuity and generalized Kirchhoff rule conditions are imposed. Applying an analytical approach based on matching soliton solutions at the vertex, we derive the sum rule for the nonlinearities of the coupled nonlinear Klein-Gordon equations on the metric star graph. This sum rule yields soliton solutions that pass through the vertex without reflection. Furthermore, it is shown that the functional forms of the conservation laws are preserved for the considered soliton solutions on metric star graphs.
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