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

Mathematics

Valipuram Manoranjan¹  Lewa’ Alzaleq²  Baha Alzalg³ 

[1] Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA;Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan;Department of Mathematics, The University of Jordan, Amman 11942, Jordan;

关键词: generalized SIdV equation;    auxiliary equation method;    exact traveling waves;    solitary waves—kink and bell types;    periodic waves;    peakon;   

DOI  :  10.3390/math10030414

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown