An attempt to study cnoidal and solitary waves in the bloodstream using computer mathematics Maple
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Keywords

Korteweg-de Vries equation
solitons
bloodstream modeling
traveling waves
Jacobi’s elliptic functions
computer mathematics

How to Cite

Chuiko, G., Dvornik, O., & Darnapuk, Y. (2020). An attempt to study cnoidal and solitary waves in the bloodstream using computer mathematics Maple. Computer Science and Engineering, 1(1), 20-28. https://doi.org/10.26693/cse2020.01.020

Abstract

Korteweg-de Vries equation and its modified shape were studied with Maple, a system of computer mathematics. We derived and dealt with their dimensionless forms. The traveling wave type solutions were found in both cases. These waves based on different Jacobi’s elliptic functions. Conditions, formulated for both models from bloodstream description in vessels, are fulfilled regarding these waves. Note, that the traveling waves within both models are similar enough, despite vital diversities found with Maple. First, they have the same periodicity, which depends on the elliptic module (0 ≤ m ≤ 1). Second, they have similar behavior in the harmonic and soliton limits (m = 0 and m = 1). Finally, they have similar dispersion relations.

https://doi.org/10.26693/cse2020.01.020
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References

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