More Solutions of Coupled Equal Width Wave Equations Arising in Plasma and Fluid Dynamics

The goal of this study is to get new analytical solutions for the system of (1+1)-coupled equal width wave equations, which describe physical processes in turbulence and other unstable coupled systems. The system is reduced to an equivalent system of ordinary differential equations using the Lie symmetries. The reduced system after a suitable choice of arbitrary constants is solved by the Sine-Cosine method for getting final solutions. Observations and comparison with reported results ((Chauhan et al. (2020) Int J Appl Comput Math 6(159):1–17), (Pandir and Ulusoy (2012) J Math 2013(1–6):201276), (EL-Sayed et al. (2014) Int J Adv Appl Math Mech 2(1):19– 25) and Raslan et al (2017) J Egypt Math Soc 25 , 350–354) confirm the novelty of solutions. Finally, trigonometric and travelling wave solutions are obtained. The resulting solutions include elastic multi solitons, multi solitons kink waves, and undular bore types, which differ from reported works. Additionally, conserved vectors are calculated for the first time in this study, revealing that the system is completely integrable.