TY - JOUR
ID - 16546
TI - Novel traveling wave solutions of generalized seventh-order KdV equation and related equation
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Hedli, Riadh
AU - Berrimi, Fella
AD - Department of Mathematics
Faculty of Sciences
University of Ferhat Abbas Setif 1
Algeria.
AD - Department of Computer Science
Faculty of Sciences
University of Ferhat Abbas Setif 1
Algeria.
Y1 - 2024
PY - 2024
VL - 12
IS - 2
SP - 392
EP - 412
KW - Nonlinear evolution equation
KW - Generalized seventh-order Korteweg-de Vries equation
KW - Traveling wave solution
KW - $\exp (-\varphi (\xi ))$-expansion method
KW - $(G^{'}/G) $-expansion method
DO - 10.22034/cmde.2023.53478.2254
N2 - In this paper, we acquire novel traveling wave solutions of the generalized seventh-order Kortewegâ€“de Vries equation and the seventh-order Kawahara equation as a special case with physical interest. Primarily, we use the advanced $\exp (-\varphi (\xi ))$-expansion method to find new exact solutions of the first equation, by considering two auxiliary equations. Then, we attain some exact solutions of the seventh-order Kawahara equation by using this method with another auxiliary equation, and also using the modified $(G^{'}/G) $-expansion method, where G satisfies a second-order linear ordinary differential equation. Additionally, utilizing the recent scientific instruments, the 2D, 3D, and contour plots are displayed. The solutions obtained in this paper include bright solitons, dark solitary wave solutions, and multiple dark solitary wave solutions. It is shown that these two methods provide an effective mathematical tool for solving nonlinear evolution equations arising in mathematical physics and engineering.
UR - https://cmde.tabrizu.ac.ir/article_16546.html
L1 - https://cmde.tabrizu.ac.ir/article_16546_f7411380cfa2b0e82eb35fada95a1c9f.pdf
ER -