A discrete generalization of the extended simplest equation method |
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| Institution: | 1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Catalonia, 08193 Bellaterra, Spain;2. Departamento de Matemática, Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, Avenida Trabalhador São Carlense, São Carlos, SP, 400, 13566-590, Brazil;3. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Lisboa 1049-001, Portugal |
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| Abstract: | We modified the so-called extended simplest equation method to obtain discrete traveling wave solutions for nonlinear differential-difference equations. The Wadati lattice equation is chosen to illustrate the method in detail. Further discrete soliton/periodic solutions with more arbitrary parameters, as well as discrete rational solutions, are revealed. We note that using our approach one can also find in principal highly accurate exact discrete solutions for other lattice equations arising in the applied sciences. |
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