kdv6 equation
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2019 ◽  
Vol 29 (11) ◽  
pp. 4205-4212
Author(s):  
Abdul-Majid Wazwaz ◽  
Gui-Qiong Xu

Purpose The purpose of this paper is to develop a new time-dependent KdV6 equation. The authors derive multiple soliton solutions and multiple complex soliton solutions for a time-dependent equation. Design/methodology/approach The newly developed time-dependent model has been handled by using the Hirota’s direct method. The authors also use the complex Hirota’s criteria for deriving multiple complex soliton solutions. Findings The examined extension of the KdV6 model exhibits complete integrability for any analytic time-dependent coefficient. Research limitations/implications The paper presents a new efficient algorithm for constructing extended models which give a variety of multiple real and complex soliton solutions. Practical implications The paper introduced a new time-dependent KdV6 equation, where integrability is emphasized for any analytic time-dependent function. Social implications The findings are new and promising. Multiple real and multiple complex soliton solutions were formally derived. Originality/value This is an entirely new work where a new time-dependent KdV6 equation is established. This is the first time that the KdV6 equation is examined as a time-dependent equation. Moreover, the complete integrability of this newly developed equation is emphasized via using Painlevé test.



2018 ◽  
Vol 11 (4) ◽  
pp. 631-641 ◽  
Author(s):  
María Santos Bruzón ◽  
◽  
Tamara María Garrido




2015 ◽  
Vol 80 (1-2) ◽  
pp. 387-396 ◽  
Author(s):  
Mohammad Mirzazadeh ◽  
Mostafa Eslami ◽  
Anjan Biswas


2013 ◽  
Vol 73 ◽  
pp. 119-125 ◽  
Author(s):  
Houria Triki ◽  
Daniela Milovic ◽  
Anjan Biswas


2011 ◽  
Vol 218 (6) ◽  
pp. 2968-2972 ◽  
Author(s):  
P.R. Gordoa ◽  
A. Pickering ◽  
J. Prada
Keyword(s):  


2011 ◽  
Vol 217 (13) ◽  
pp. 6230-6236 ◽  
Author(s):  
Yi Zhang ◽  
Xiao-lan Dang ◽  
Hong-xian Xu


2010 ◽  
Vol 54 (6) ◽  
pp. 962-964 ◽  
Author(s):  
Da-Feng Zuo
Keyword(s):  


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