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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


A Method for Solving Nonlinear Differential Equations: An Application to λφ4 Model

Discontinuity, Nonlinearity, and Complexity 4(2) (2016) 163--171 | DOI:10.5890/DNC.2016.06.004

Danilo V. Ruy

Instituto de Física Teórica-UNESP, Rua Dr Bento Teobaldo Ferraz 271, Bloco II São Paulo, 01140-070, Brazil

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Abstract

Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad′e approximants for solving nonlinear partial differential equations without requiring a one-dimensional reduction. This method is applied to the λφ4 model in 4 dimensions and new solutions are obtained.

Acknowledgments

I am thankful to H. Aratyn, J. F. Gomes and A. H. Zimerman for discussions. The author also thanks FAPESP (2010/18110-9) for financial support.

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