AN INSIGHT ON THE (2 + 1)-DIMENSIONAL FRACTAL NONLINEAR BOITI–LEON–MANNA–PEMPINELLI EQUATIONS
Jian-She Sun
Abstract
With the aid of a new fractal derivative, the nonlinear Boiti–Leon–Manna–Pempinelli equation (NBLMPE) with nonsmooth boundary is explored. The variational principle of the fractal NBLMPE is successfully established by fractal wave transformation (FWT) and fractal semi-inverse method (SIM) and strong minimum condition of fractal NBLMPE is proven with the fractal Weierstrass theorem. Based on the two-scale transformation method (TSTM) and homogeneous equilibrium method (HBM), soliton-like solutions for the [Formula: see text]-dimensional (SLS [Formula: see text]D) fractal NBLMPE are acquired. A powerful means of coupling HBM and TSTM to solve fractal differential equations is proposed.
Topics & Concepts
FractalFractal derivativeMathematicsMathematical analysisTransformation (genetics)Nonlinear systemFractal dimension on networksApplied mathematicsFractal dimensionFractal analysisPhysicsQuantum mechanicsChemistryBiochemistryGeneFractional Differential Equations SolutionsNonlinear Waves and SolitonsNumerical methods in engineering