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Exact Traveling Waves of a Generalized Scale-Invariant Analogue of the Korteweg–de Vries Equation

Author

Listed:
  • Lewa’ Alzaleq

    (Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan)

  • Valipuram Manoranjan

    (Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA)

  • Baha Alzalg

    (Department of Mathematics, The University of Jordan, Amman 11942, Jordan
    Department of Computer Science and Engineering, The Ohio State University, Columbus, OH 43210, USA)

Abstract

In this paper, we study a generalized scale-invariant analogue of the well-known Korteweg–de Vries (KdV) equation. This generalized equation can be thought of as a bridge between the KdV equation and the SIdV equation that was discovered recently, and shares the same one-soliton solution as the KdV equation. By employing the auxiliary equation method, we are able to obtain a wide variety of traveling wave solutions, both bounded and singular, which are kink and bell types, periodic waves, exponential waves, and peaked (peakon) waves. As far as we know, these solutions are new and their explicit closed-form expressions have not been reported elsewhere in the literature.

Suggested Citation

  • Lewa’ Alzaleq & Valipuram Manoranjan & Baha Alzalg, 2022. "Exact Traveling Waves of a Generalized Scale-Invariant Analogue of the Korteweg–de Vries Equation," Mathematics, MDPI, vol. 10(3), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:414-:d:736605
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