Exact traveling wave solutions of the stochastic Wick-type fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

Jin Hyuk Choi; Hyunsoo Kim; Jin Hyuk Choi; Hyunsoo Kim

doi:10.3934/math.2021240

AIMS Mathematics

2021, Volume 6, Issue 4: 4053-4072. doi: 10.3934/math.2021240

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Research article

Exact traveling wave solutions of the stochastic Wick-type fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

Jin Hyuk Choi ¹,
Hyunsoo Kim ^{2
,
,}

1.
Humanitas College, Kyung Hee University, Yongin, 17104, Republic of Korea
2.
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea

Received: 06 November 2020 Accepted: 18 January 2021 Published: 04 February 2021
MSC : 35C07, 35K57

In this work, we test the intgrability of the stochastic Wick-type fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation on the Painlevé test and construct new Wick-type and nob-Wick-type versions of exact traveling wave solutions of the stochastic Wick-type fractional CDGSK equation by employing the Hermit transformation, the conformable fractional derivative and the sub-equations method. Moreover, we obtain exact traveling wave solutions of the fractional Sawada-Kotera (SK) equation and the fractional Caudrey-Dodd-Gibbon (CDG) equation as well. It is note that physical illustration may be useful to predict internal structure of the considered equations. The results confirm that sub-equations method is very effective and efficient to find exact traveling wave solutions of Wick-type fractional nonlinear evolution equations.
- CDGSK equation,
- Painlevé test,
- Hermite transformatiom,
- conformable fractional derivative,
- sub-equations method
Citation: Jin Hyuk Choi, Hyunsoo Kim. Exact traveling wave solutions of the stochastic Wick-type fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation[J]. AIMS Mathematics, 2021, 6(4): 4053-4072. doi: 10.3934/math.2021240

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Abstract

In this work, we test the intgrability of the stochastic Wick-type fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation on the Painlevé test and construct new Wick-type and nob-Wick-type versions of exact traveling wave solutions of the stochastic Wick-type fractional CDGSK equation by employing the Hermit transformation, the conformable fractional derivative and the sub-equations method. Moreover, we obtain exact traveling wave solutions of the fractional Sawada-Kotera (SK) equation and the fractional Caudrey-Dodd-Gibbon (CDG) equation as well. It is note that physical illustration may be useful to predict internal structure of the considered equations. The results confirm that sub-equations method is very effective and efficient to find exact traveling wave solutions of Wick-type fractional nonlinear evolution equations.

References

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