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

Lewa’ Alzaleq, Valipuram Manoranjan and Baha Alzalg
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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

Mathematics, 2022, vol. 10, issue 3, 1-18

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.

Keywords: generalized SIdV equation; auxiliary equation method; exact traveling waves; solitary waves—kink and bell types; periodic waves; peakon (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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