Around Chaotic Disturbance and Irregularity for Higher Order Traveling Waves

Many unknown features in the theory of wave motion are still captivating the global scientific community. In this paper, we consider a model of seventh order Korteweg–de Vries (KdV) equation with one perturbation level, expressed with the recently introduced derivative with nonsingular kernel, Caput...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2018-01, Vol.2018 (2018), p.1-11
Main Authors: Doungmo Goufo, Emile Franc, Tchangou Toudjeu, Ignace
Format: Article
Language:English
Subjects:
Applied mathematics
Computer simulation
Integral equations
Irregularities
Mathematical models
Mathematics
Perturbation methods
Physics
Solitary waves
Traveling waves
Waves
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Summary:Many unknown features in the theory of wave motion are still captivating the global scientific community. In this paper, we consider a model of seventh order Korteweg–de Vries (KdV) equation with one perturbation level, expressed with the recently introduced derivative with nonsingular kernel, Caputo-Fabrizio derivative (CFFD). Existence and uniqueness of the solution to the model are established and proven to be continuous. The model is solved numerically, to exhibit the shape of related solitary waves and perform some graphical simulations. As expected, the solitary wave solution to the model without higher order perturbation term is shown via its related homoclinic orbit to lie on a curved surface. Unlike models with conventional derivative (γ=1) where regular behaviors are noticed, the wave motions of models with the nonsingular kernel derivative are characterized by irregular behaviors in the pure factional cases (γ
ISSN:2314-4629
2314-4785
DOI:10.1155/2018/2391697