Abstract
A new variety of (3+1)-dimensional Korteweg–de Vries equations are developed. The recursion operator of the Korteweg–de Vries equation is used to derive these higher dimensional integrable models. We establish a generalized dispersion relation and a generalized form for the one soliton solutions. The new equations generate distinct solitons structures and distinct dispersion relations as well.
This is a preview of subscription content, log in via an institution to check access.
References
F J Olver J. Math. Phys. 18 1212 (1977)
J A Sanders and J P Wang Nonlinear Anal. 47 5213 (2001)
J P Wang J. Nonlinear Math. Phys. 9 213 (2002)
S Lou Commun. Theor. Phys. 28 41 (1997)
F Magri Lectures Notes in Physics (Berlin: Springer) (1980)
A R Adem and C M Khalique Nonlinear Anal. Real World Appl. 13 1692 (2012)
A R Adem and C M Khalique Comput. Fluids 81 10 (2013)
M Molati and C M Khalique Appl. Math. Comput. 219 7917 (2013)
D Baldwin and W Hereman Int. J. Comput. Math. 87 1094 (2010)
M Dehghan and R Salehi Appl. Math. Model 36 1939 (2012)
A S Fokas Stud. Appl. Math. 77 253 (1987)
R Hirota The Direct Method in Soliton Theory (Cambridge: Cambridge University Press) (2004)
A M Wazwaz Partial Differential Equations and Solitary Waves Theorem (Berlin: Springer) (2009)
A M Wazwaz Phys. Scr. 84 035001 (2011)
A M Wazwaz Phys. Scr. 86 065007 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wazwaz, A.M. A variety of (3+1)-dimensional KdV equations derived by using the KdV recursion operator. Indian J Phys 90, 577–582 (2016). https://doi.org/10.1007/s12648-015-0795-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12648-015-0795-4