Factorization method for some inhomogeneous Liénard equations

• O. Cornejo-Pérez ^[1] ; S.C. Mancas ^[2] ; H.C. Rosu ^[3] ; C.A. Rico-Olvera ^[1]
  1. [1] Universidad Autónoma de Querétaro

     Universidad Autónoma de Querétaro

     México

     
  2. [2] Embry–Riddle Aeronautical University

     Embry–Riddle Aeronautical University

     Estados Unidos

     
  3. [3] IPICyT, Instituto Potosino de Investigación Científica y Tecnológica, San Luis Potosí, México

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• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 67, Nº. 3, 2021, págs. 443-446
• Idioma: inglés
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• Resumen

  • We obtain closed-form solutions of several inhomogeneous Li ́enard equations by the factorization method. The two factorization conditionsinvolved in the method are turned into a system of first-order differential equations containing the forcing term. In this way, one can findthe forcing terms that lead to integrable cases. Because of the reduction of order feature of factorization, the solutions are simultaneouslysolutions of first-order differential equations with polynomial nonlinearities. The illustrative examples of Li ́enard solutions obtained in thisway generically have rational parts, and consequently display singularities.