Non-linear water waves (KdV) equation by Painlevé property and Schwarzian derivative | Zendy

Miodrag Mateljević | Zendy; Attia Mostafa | Zendy

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Non-linear water waves (KdV) equation by Painlevé property and Schwarzian derivative

Author(s) -

Miodrag Mateljević,

Attia Mostafa

Publication year - 2017

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1712627m

Subject(s) - korteweg–de vries equation , schwarzian derivative , mathematics , partial differential equation , nonlinear system , mathematical analysis , work (physics) , differential equation , derivative (finance) , physics , economics , quantum mechanics , financial economics , thermodynamics

The Korteweg-de Vries (KdV) equation, a nonlinear partial differential equation which describes the motion of water waves, has been of interest since John Scott Russell (1844) [1]. In present work we study this kind of equation and through our study we found that the KdV equation passes Painleve’s test, but we could not locate the solution directly, so we used Schwartizian derivative technique. Therefore, we were able to find two new exact solutions to the KdV equation. Also, we used the numerical method of Modified Zabusky-Kruskal to describe the behavior of these solutions.

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