EXACT TRAVELING WAVE SOLUTION FOR THE FRACTAL RIEMANN WAVE MODEL ARISING IN OCEAN SCIENCE
Wang Kang-le
Abstract
In this paper, we investigate the Riemann wave model (RWM) on Cantor sets by using the local fractional derivative (LFD). A novel computational approach is provided to seek the exact traveling-wave solution of the non-differential type for the local fractional Riemann wave model (LFRWM). The proposed scheme is called local fractional traveling-wave method (LFTWM). An example is given to illustrate that the LFTWM is simple and excellent. The properties of the obtained traveling-wave solutions are elaborated by some 3D graphs. The LFTWM sheds a new light on solving the local fractional wave equations (LFWE) in physics and engineering.
Topics & Concepts
FractalMathematicsFractional calculusRiemann problemMathematical analysisSimple (philosophy)Traveling waveRiemann hypothesisApplied mathematicsEpistemologyPhilosophyFractional Differential Equations SolutionsNonlinear Waves and SolitonsDifferential Equations and Numerical Methods