Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations |
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Authors: | Stefan C. Mancas Haret C. Rosu |
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Affiliation: | 1. Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900, USA;2. IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP, Mexico |
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Abstract: | We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations. |
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Keywords: | Abel equations Integrability Dissipative nonlinear equations |
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