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; Exterior; Epsilon; PDEtools; DDESpecialSolutions; Rif; PainleveTest; GiNaC; GiNaCDE; hypergeometricsols; DLMF; JACOBI; BVPh; Matlab Cited in: 65 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. Zbl 1137.35324Baldwin, D.; Göktaş, Ü.; Hereman, W.; Hong, L.; Martino, R. S.; Miller, J. C. 2004 all top 5 Cited by 79 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, Fei 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 all top 5 Cited in 32 Serials 18 Applied Mathematics and Computation 4 Computers & Mathematics with Applications 4 Chaos, Solitons and Fractals 4 Communications in Nonlinear Science and Numerical Simulation 3 Physics Letters. A 2 Computer Physics Communications 2 Journal of Computational and Applied Mathematics 2 Applied Mathematical Modelling 2 Advances in Mathematical Physics 1 International Journal of Modern Physics B 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal of Theoretical Physics 1 Journal of Mathematical Analysis and Applications 1 Reports on Mathematical Physics 1 Chinese Annals of Mathematics. Series B 1 Journal of Symbolic Computation 1 Mathematical and Computer Modelling 1 Numerical Algorithms 1 Computational Mathematics and Mathematical Physics 1 International Journal of Computer Mathematics 1 Computational and Applied Mathematics 1 Engineering Analysis with Boundary Elements 1 Mathematical Problems in Engineering 1 Nonlinear Dynamics 1 Boletín de Matemáticas. Nueva Serie 1 Nonlinear Analysis. Real World Applications 1 International Journal of Applied Mathematics and Mechanics 1 International Journal of Contemporary Mathematical Sciences 1 Discrete and Continuous Dynamical Systems. Series S 1 Differential Equations and Applications 1 International Journal of Differential Equations 1 Symmetry all top 5 Cited in 12 Fields 55 Partial differential equations (35-XX) 19 Numerical analysis (65-XX) 9 Ordinary differential equations (34-XX) 7 Computer science (68-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Fluid mechanics (76-XX) 2 Quantum theory (81-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year