Similarity solutions of the super KdV equation

1995 ◽  
Vol 16 (9) ◽  
pp. 901-904 ◽  
Author(s):  
Yu Huidan ◽  
Zhang Jiefang
Keyword(s):  
Kdv Equation ◽  
Similarity Solutions ◽  
Super Kdv Equation

Towards an integrable N=3 super KdV equation

1993 ◽  
Vol 173 (2) ◽  
pp. 143-147
Author(s):  
Stefano Bellucci ◽  
Evgenyi Ivanov ◽  
Sergey Krivonos
Keyword(s):  
Kdv Equation ◽  
Super Kdv Equation

Symmetry operators and exact solutions of a type of time-fractional Burgers–KdV equation

2019 ◽  
Vol 16 (02) ◽  
pp. 1950032 ◽  
Author(s):  
Azadeh Naderifard ◽  
S. Reza Hejazi ◽  
Elham Dastranj ◽  
Ahmad Motamednezhad
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Vector Fields ◽  
Kdv Equation ◽  
Group Analysis ◽  
Invariant Subspaces ◽  
Similarity Solutions ◽  
Optimal System ◽  
Lie Point Symmetries ◽  
Symmetry Operators

In this paper, group analysis of the fourth-order time-fractional Burgers–Korteweg–de Vries (KdV) equation is considered. Geometric vector fields of Lie point symmetries of the equation are investigated and the corresponding optimal system is found. Similarity solutions of the equation are presented by using the obtained optimal system. Finally, a useful method called invariant subspaces is applied in order to find another solutions.

Symmetries for the super-KdV equation

1988 ◽  
Vol 21 (11) ◽  
pp. L579-L584 ◽  
Author(s):  
P H M Kersten ◽  
P K H Gragert
Keyword(s):  
Kdv Equation ◽  
Super Kdv Equation

scholarly journals On the Korteweg-de Vries equation: an associated equation

1984 ◽  
Vol 7 (2) ◽  
pp. 263-277 ◽  
Author(s):  
Eugene P. Schlereth ◽  
Ervin Y. Rodin
Keyword(s):  
Initial Value Problems ◽  
Vries Equation ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equation ◽  
Inverse Scattering Transform ◽  
Similarity Solutions ◽  
Airy Functions ◽  
Initial Value ◽  
Scattering Transform ◽  
De Vries

The purpose of this paper is to describe a relationship between the Korteweg-de Vries (KdV) equationut−6uux+uxxx=0and another nonlinear partial differential equation of the formzt+zxxx−3zxzxxz=H(t)z.The second equation will be called the Associated Equation (AE) and the connection between the two will be explained. By considering AE, explicit solutions to KdV will be obtained. These solutions include the solitary wave and the cnoidal wave solutions. In addition, similarity solutions in terms of Airy functions and Painlevé transcendents are found. The approach here is different from the Inverse Scattering Transform and the results are not in the form of solutions to specific initial value problems, but rather in terms of solutions containing arbitrary constants.

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