Solitary waves travelling along an unsmooth boundary
Ji‐Huan He, Na Qie, Chun‐Hui He
Abstract
It is well-known that the boundary conditions will greatly affect the wave shape of a nonlinear wave equation. This paper reveals that the peak of a solitary wave is weakly affected by the unsmooth boundary. A fractal Korteweg-de Vries (KdV) equation is used as an example to show the solution properties of a solitary wave travelling along an unsmooth boundary. A fractal variational principle is established in a fractal space and its solitary wave solution is obtained, and its wave shape is discussed for different fractal dimensions of the boundary.
Topics & Concepts
FractalKorteweg–de Vries equationBoundary (topology)Mathematical analysisBoundary value problemNonlinear systemSpace (punctuation)PhysicsMathematicsClassical mechanicsQuantum mechanicsComputer scienceOperating systemNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems