A generalized Weierstrass elliptic function expansion method for solving some nonlinear partial differential equations

The present paper deals with families of non-trivial solutions of the equation ( d d ξ w ) 2 = P w 4 ( ξ ) + Q w 2 ( ξ ) + R . On the basis of these solutions, a direct and generalized algebraic algorithm is described for constructing the new solutions of some nonlinear partial differential equation...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) Vol. 58; no. 9; pp. 1725 - 1735
Main Authors: Saied, E.A., Abd El-Rahman, Reda G., Ghonamy, Marwa I.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.11.2009
Subjects:
First-kind elliptic equation
KP equation
mKdV equation
Periodic solutions
Weierstrass elliptic function solutions
Weierstrass elliptic function solutions
First-kind elliptic equation
KP equation
mKdV equation
Periodic solutions
ISSN:0898-1221, 1873-7668
Online Access:Get full text
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Summary:The present paper deals with families of non-trivial solutions of the equation ( d d ξ w ) 2 = P w 4 ( ξ ) + Q w 2 ( ξ ) + R . On the basis of these solutions, a direct and generalized algebraic algorithm is described for constructing the new solutions of some nonlinear partial differential equations (NLPDEs). Subsequently, many new and more general exact solutions in terms of the Weierstrass elliptic function ℘ ( ξ ; g 2 , g 3 ) are obtained. The method can be applied to other NLPDEs in mathematical physics.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2009.05.025