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Dispersive of propagation wave solutions to unidirectional shallow water wave Dullin–Gottwald–Holm system and modulation instability analysis
Author(s) -
Bilal M.,
Seadawy Aly R.,
Younis M.,
Rizvi S. T. R.,
Zahed Hanadi
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7013
Subject(s) - mathematics , waves and shallow water , norm (philosophy) , instability , shock wave , mathematical analysis , constraint (computer aided design) , plane wave , plane (geometry) , mechanics , geometry , physics , optics , political science , law , thermodynamics
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.