TY - JOUR
TI - Variational approach for the fractal generalized Bogoyavlensky-Konopelchenko equation
AU - Sun Yi
AU - Lu Jun-Feng
JN - Thermal Science
PY - 2026
VL - 30
IS - 2
SP - 837
EP - 846
PT - Article
AB - This paper explores a fractal generalized Bogoyavlensky-Konopelchenko  equation (gBK) defined by He's fractal derivative. Employing the  variational aproach in conjunction with the two-scale fractal  transformation has yielded the fractal wave solutions. Furthermore, we offer  remarks on the variational formulation of the conventional gBK equation  presented in previous literature. Notably, we have identified two novel  solutions: the fractal periodic wave solution and the fractal bright soliton  solution. These solutions have not been previously explored in the existing  literature. The propagation behavior of these fractal wave solutions is  vividly demonstrated through 3-D figures with diverse fractal dimensions  and amplitudes. The findings of the present study contribute to the  theoretical research on the gBK equation and provide valuable insights for  future studies in the field of fractal differential equations.
DO - 10.2298/TSCI2602837S
ER -