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Kumar, Raj; Kumar, Avneesh

More solutions of coupled equal width wave equations arising in plasma and fluid dynamics. (English) Zbl 1513.35036

Int. J. Appl. Comput. Math. 8, No. 4, Paper No. 186, 13 p. (2022).
Summary: 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 [S. Chauhan et al., Int. J. Appl. Comput. Math. 6, No. 6, Paper No. 159, 17 p. (2020; Zbl 1465.35096); Y. Pandir and H. Ulusoy, J. Math. 2013, Article ID 201276, 5 p. (2013; Zbl 1273.35018); M. F. El-Sayed et al., Int. J. Adv. Appl. Math. Mech. 2, No. 1, 19–25 (2014; Zbl 1359.35017) and K. R. Raslan et al., J. Egypt. Math. Soc. 25, No. 3, 350–354 (2017; Zbl 1377.35052)] confirm the novelty of solutions. Finally, trigonometric and traveling 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.

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
22E70 Applications of Lie groups to the sciences; explicit representations
35C07 Traveling wave solutions

Keywords:

Lie symmetry analysis; coupled equal width wave equations; traveling wave; nonlinear evolution equations; conserved vectors

Citations:

Zbl 1465.35096; Zbl 1273.35018; Zbl 1359.35017; Zbl 1377.35052
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Full Text: DOI

References:

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