TY - JOUR
TI - Variational principle and periodic wave solutionals for elastic rod equation with fractal derivative
AU - Tian Yi
JN - Thermal Science
PY - 2025
VL - 29
IS - 3
SP - 1871
EP - 1881
PT - Article
AB - The present research paper will demonstrate the variational principle and  periodic wave solutions of the elastic rod equation. First, we will  illustrate the generalized variational principle in two examples. Secondly,  we consider a fractal non-linear elastic rod equation with an unsmooth  boundary. Based on two-scale fractal theory and the semi-inverse method, we  successfully establish the fractal variational principle for the non-linear  elastic rod equation. This is helpful for studying symmetry, finding  conserved quantities, and revealing possible traveling solution structures  of the equation. Finally, we investigate periodic wave solutions of the  non-linear elastic rod equation