NEW SOLITARY WAVE SOLUTIONS OF THE FRACTIONAL MODIFIED KdV–KADOMTSEV–PETVIASHVILI EQUATION
Kang‐Le Wang
Abstract
This work suggests a fractional modification of the KdV–Kadomtsev–Petviashvili model with the beta-derivative to consider unsmooth boundary. Some new interesting solitary waves are found for the first time ever by the fractional sine–cosine method and the fractional ansatz method. These dynamical characteristics of new solitary waves are discussed by some three-dimensional (3D) figures, and the effect of the fractal parameters on the solitary waves traveling is also discussed and explained.
Topics & Concepts
Korteweg–de Vries equationAnsatzMathematicsFractional calculusFractalMathematical analysisWork (physics)SineTrigonometric functionsMathematical physicsTraveling wavePhysicsNonlinear systemGeometryQuantum mechanicsNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems