Explicit Lump Solitary Wave of Certain Interesting (3+1)-Dimensional Waves in Physics via Some Recent Traveling Wave Methods

• Published in: Entropy (Basel, Switzerland) Vol. 21; no. 4; p. 397
• Main Authors: Khater, Mostafa M. A., Attia, Raghda A. M., Lu, Dianchen
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 15-04-2019; MDPI
• Subjects: Calculus; complex lump solitary wave solutions; Continuity (mathematics); Derivatives; Exact solutions; explicit lump solitary wave solutions; Fractals; fractional Jimbo–Miwa (JM) equation; Methods; Nonlinear differential equations; Ordinary differential equations; Partial differential equations; Physics; Solitary waves; Traveling waves
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e21040397

This study investigates the solitary wave solutions of the nonlinear fractional Jimbo–Miwa (JM) equation by using the conformable fractional derivative and some other distinct analytical techniques. The JM equation describes the certain interesting (3+1)-dimensional waves in physics. Moreover, it is considered as a second equation of the famous Painlev’e hierarchy of integrable systems. The fractional conformable derivatives properties were employed to convert it into an ordinary differential equation with an integer order to obtain many novel exact solutions of this model. The conformable fractional derivative is equivalent to the ordinary derivative for the functions that has continuous derivatives up to some desired order over some domain (smooth functions). The obtained solutions for each technique were characterized and compared to illustrate the similarities and differences between them. Profound solutions were concluded to be powerful, easy and effective on the nonlinear partial differential equation.