AN INSIGHT ON THE (2 + 1)-DIMENSIONAL FRACTAL NONLINEAR BOITI–LEON–MANNA–PEMPINELLI EQUATIONS

Jianshe Sun
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Jianshe Sun: Institute of Mathematics and Interdisciplinary Science, Jiaozuo Teacher’s College, Jiaozuo 454150, P. R. China2School of Mathematics, Jiaozuo Teacher’s College, Jiaozuo 454150, P. R. China3School of Mathematics, China University of Mining and Technology, Xuzhou 221116, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 09, 1-9

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 (2 + 1)-dimensional (SLS (2 + 1)D) fractal NBLMPE are acquired. A powerful means of coupling HBM and TSTM to solve fractal differential equations is proposed.

Keywords: Fractal Derivative; Fractal Semi-inverse Method; Variational Principle; Boiti–Leon Manna–Pempinelli Equation; Two-scale Transform Method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501882

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