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New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations

Hadi Rezazadeh

Hadi Rezazadeh

Faculty of Engineering Technology, Amol University of Special Modern TechnologiesAmol, Iran
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Rezazadeh, Hadi
, 
Alper Korkmaz

Alper Korkmaz

Weimar, Germany
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Korkmaz, Alper
, 
Abdelfattah EL Achab

Abdelfattah EL Achab

Faculty of Sciences Semlalia, Department of Mathematics, Cadi Ayyad UniversityMarrakech, Morocco
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EL Achab, Abdelfattah
, 
Waleed Adel

Waleed Adel

Faculty of Engineering, Department of Mathematics and Engineering Physics, Mansoura UniversityEgypt
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Adel, Waleed
 and 
Ahmet Bekir

Ahmet Bekir

Eskisehir, Turkey
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Bekir, Ahmet
  
Oct 10, 2020
New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations's Cover Image
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Published Online: Oct 10, 2020
Page range: 447 - 458
Received: Mar 09, 2020
Accepted: Sep 23, 2020
DOI: https://doi.org/10.2478/amns.2020.2.00034
Keywords
© 2020 Hadi Rezazadeh et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Graphics of the solution equation (14) (u5(x,t)) corresponding to the valuesβ = 3, α = 4, σ = 2, A = 2.65, p = 1, q = 0.9, b0 = 1 and ξ0 = −0.5 (a) 3D plot and (b) contour plot.
Graphics of the solution equation (14) (u5(x,t)) corresponding to the valuesβ = 3, α = 4, σ = 2, A = 2.65, p = 1, q = 0.9, b0 = 1 and ξ0 = −0.5 (a) 3D plot and (b) contour plot.

Fig. 2

Graphics of the solution equation (28) (u14(x,t)) corresponding to the valuesλ = 1.5, m = 3, A = 2.7, p = 1.2, q = 0.9, b0 = 3 and ξ0 = 1.5 (a) 3D plot and (b) contour plot.
Graphics of the solution equation (28) (u14(x,t)) corresponding to the valuesλ = 1.5, m = 3, A = 2.7, p = 1.2, q = 0.9, b0 = 3 and ξ0 = 1.5 (a) 3D plot and (b) contour plot.

Fig. 3

Graphics of the solution equation (28) (u1+(x,t)) (u_1^ + (x,t)) corresponding to the valuesβ = 4, α = 2, σ = 3, A = 2.6, p = 1, q = 0.9 and ξ0 = 0 (a) 3D plot and (b) contour plot.
Graphics of the solution equation (28) (u1+(x,t)) (u_1^ + (x,t)) corresponding to the valuesβ = 4, α = 2, σ = 3, A = 2.6, p = 1, q = 0.9 and ξ0 = 0 (a) 3D plot and (b) contour plot.

Fig. 4

Graphics of the solution equation (34) (u7-(x,t)) (u_7^ - (x,t)) corresponding to the values β = 3, α = 1, σ = 2, A = e, p = 1, q = 1 and ξ0 = 0 (a) 3D plot and (b) contour plot.
Graphics of the solution equation (34) (u7-(x,t)) (u_7^ - (x,t)) corresponding to the values β = 3, α = 1, σ = 2, A = e, p = 1, q = 1 and ξ0 = 0 (a) 3D plot and (b) contour plot.
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