New analytical wave solitons and some other wave solutions of truncated M-fractional LPD equation along parabolic law of non-linearity

• Published in: Optical and quantum electronics Vol. 55; no. 7
• Main Authors: Raheel, M., Zafar, Asim, Razzaq, Waseem, Qousini, Maysoon, Almusawa, Musawa Yahya
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2023; Springer Nature B.V
• Subjects: Characterization and Evaluation of Materials; Computer Communication Networks; Electrical Engineering; Lasers; Nonlinear differential equations; Optical Devices; Optics; Partial differential equations; Photonics; Physics; Physics and Astronomy; Solitary waves; The; Truncated M-fractional derivative; function; The extended sinh-Gordon equation expansion scheme; Hirota bilinear scheme; Parabolic law; Laksmanan–Porsezian–Daniel equation
• ISSN: 0306-8919; 1572-817X
• DOI: 10.1007/s11082-023-04868-9

This article is about, the new analytical wave solitons, breather-wave, lump-kink and interaction between lump-kink and rogue wave solutions of Laksmanan–Porsezian–Daniel equation with parabolic law along a new definition of derivative has been explored. For this purpose, the exp a function, the extended sinh-Gordon equation expansion scheme and Hirota bilinear schemes have been utilized. The resulting solutions are dark, bright, dark-bright, periodic, singular and other kinds of solitons. These results are obtained and also verified by Mathematica and Maple tools. Our gained solutions are newer than the existing results in the literature. Some of the gained results are explained by 2-dimensional, 3-dimensional and contour plots. Results may be useful for the progress of the model in further study. The schemes used in this research are effective, easy and reliable to handle the other fractional nonlinear partial differential equations.