EXACT SOLUTIONS OF GENERALIZED KORTEWEG-DE VRIES EQUATIONS WITH VARIABLE COEFFICIENTS
DOI:
https://doi.org/10.15407/dopovidi2023.06.003Keywords:
Korteweg-de Vries equations, exact solutions, equivalence groupoid, admissible transformations, equivalence methodAbstract
The transformational properties of two classes of generalized Korteweg-de Vries equations with coefficients depen- dent on the time variable are investigated, and the effectiveness of the equivalence method for constructing exact solutions of such equations is demonstrated. Specifically, the equivalence groupoids for both classes of equations are identified, and it is proven that both classes are normalized. A criterion for the reducibility of variable coeffi- cient equations from one of the classes to the standard modified Korteweg-de Vries equation is established. For the second class of equations, full similarity to the classic Korteweg-de Vries equation is demonstrated. It is shown that the equivalence method of finding exact solutions is more effective for such classes of equations compared to meth- ods employed by other authors. Consequently, formulas for generating exact solutions of generalized Korteweg-de Vries equations with variable coefficients are obtained, and examples of constructing exact solutions using these formulas are presented.
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