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PDESpecialSolutions

swMATH ID: 12342
Software Authors: Baldwin, D.; Göktaş, Ü.; Hereman, W.; Hong, L.; Martino, R.S.; Miller, J.C.
Description: Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi’s elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi’s sn or cn functions. Examples illustrate key steps of the algorithms.The new algorithms are implemented in Mathematica. The package PDESpecialSolutions.m can be used to automatically compute new special solutions of nonlinear PDEs. Use of the package, implementation issues, scope, limitations, and future extensions of the software are addressed. A survey is given of related algorithms and symbolic software to compute exact solutions of nonlinear differential equations.
Homepage: http://inside.mines.edu/~whereman/software.html
Keywords: exact solutions; nonlinear PDEs; tanh method; symbolic software
Related Software: ATFM; RATH; Maple; MACSYMA; RAEEM; PDERecursionOperator; Mathematica; Epsilon; PDEtools; DDESpecialSolutions; Rif; PainleveTest; GiNaC; GiNaCDE; hypergeometricsols; DLMF; Exterior; JACOBI; BVPh; Matlab
Cited in: 65 Publications
all top 5

Cited by 78 Authors

10 Wazwaz, Abdul-Majid Abdul-Rahman
6 Kudryashov, Nikolaĭ Alekseevich
4 Khater, Ahmed H.
4 Muriel, Concepción
4 Romero, Juan Luis
3 Baldwin, Douglas E.
3 Hereman, Willy A.
3 Temsah, R. S.
2 Abraham-Shrauner, Barbara
2 Callebaut, Dirk K.
2 Göktaş, Ünal
2 Gomez Sierra, Cesar Augusto
2 Salas, Alvaro H.
2 Seadawy, Aly R.
2 Tang, Bo
1 Abdelhamid, Hamdi M.
1 Abdelwahed, H. G.
1 Abulwafa, Essam M.
1 Ali, Ijaz
1 Antoniou, Solomon M.
1 Arafa, Anas. A. M.
1 Bochkarev, Andreĭ Vladimirovich
1 Chau, Chi Kin
1 Chen, Yong
1 Dehghan Takht Fooladi, Mehdi
1 Dimitrova, Zlatinka I.
1 El-Shewy, Emad Khader
1 Elboree, Mohammed K.
1 Elmahdy, Ghada
1 Elwakil, S. A.
1 Fan, Yingzhe
1 Ganjiani, Hossein
1 Ganjiani, Mehdi
1 Gao, Yixian
1 Gómez, Cesar A.
1 He, Chunhua
1 He, Yinnian
1 Ivanova, Tsvetelina I.
1 Jeffrey, David J.
1 Jia, Huabing
1 Jin, Lin
1 Kochanov, Mark B.
1 Lakestani, Mehrdad
1 Liang, Songxin
1 Lu, Tzontzer
1 Ma, Jinli
1 Martino, R. S.
1 Methi, Giriraj
1 Mohammed, Wael W.
1 Natsis, Dimitrios G.
1 Ozis, Turgut
1 Picard, P. Y.
1 Pinar, Zehra
1 Qu, Junfeng
1 Rizvi, Syed Tahir Raza
1 S., Cesar A. Gómez
1 Sayers, Judy
1 Schürmann, Hans W.
1 Serov, Valery S.
1 Sinelshchikov, Dmitry I.
1 Siraj-ul-Islam
1 Tang, Yaning
1 Tirmizi, Syed Ikram Abbas
1 Vitanov, Nikolay K.
1 Wang, Qi
1 Wang, Xuemin
1 Wei, LeiLei
1 Xiaoyan, Tang
1 Xiazhi, Hao
1 Xu, Wei
1 Yin, Weishi
1 Yinping, Liu
1 Younis, Muhammad
1 Zeidan, Dia
1 Zemlyanukhin, Alexander I.
1 Zhang, Weipeng
1 Zhang, Xindong
1 Zhibin, Li

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