Variational approach for time-space fractal Bogoyavlenskii equation
Junfeng Lu, Shaowei Shen, Lei Chen
Abstract
In this paper, we apply the variational approach for solving the time-space fractal Bogoyavlenskii equation. By the two-scale fractal complex transformation, the fractal modification of Bogoyarlenskii equation is equivalently rewritten as the original Bogoyavlenskii equation. By variational principle, different type solutions including fractal bright soliton solution, fractal bright-like soliton solution, fractal kinky-bright soliton solution and fractal periodic wave solution are provided, which are not touched in the existing literature. Numerical results are presented to show the propagation behaviours.
Topics & Concepts
FractalSpace (punctuation)MathematicsMathematical analysisApplied mathematicsComputer scienceOperating systemFractional Differential Equations SolutionsNonlinear Waves and SolitonsDifferential Equations and Numerical Methods