Dispersive of propagation wave solutions to unidirectional shallow water wave Dullin–Gottwald–Holm system and modulation instability analysis. (4th November 2020)

• Record Type: Journal Article
• Authors: Bilal, M.; Seadawy, Aly R.; Younis, M.; Rizvi, S. T. R.; Zahed, Hanadi
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 5(2021)
• Page Start: 4094
• Page End: 4104
• Publication Date: 2020-11-04
• Subjects: direct algebraic technique -- shallow water wave -- solitons; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7013
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This article possesses modulation instability (MI) analysis and new exact wave solutions to unidirectional Dullin–Gottwald–Holm (DGH) system that describes the prorogation of waves in shallow water. The exact wave solutions in single and combined form like shock, singular, and shock‐singular are extracted by means of an innovative integration norm, namely, G ′ / G 2 ‐expansion scheme. The periodic and plane wave solutions are also emerged. The constraint conditions which ensure the existence of solutions are discussed as well. Moreover, the choice of suitable parameters gives the three‐dimensional and two‐dimensional sketches, and furthermore, their contour plots are also drawn.