Soliton-like Solutions of General Variable Coefficient Cylindrical/Spherical KdV Equation

Lingxiao Li () and Mingliang Wang
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Lingxiao Li: School of Mathematics & Statistics, Henan University of Science & Technology, Luoyang 471000, China
Mingliang Wang: School of Mathematics & Statistics, Henan University of Science & Technology, Luoyang 471000, China

Mathematics, 2022, vol. 10, issue 17, 1-8

Abstract: The general variable coefficient cylindrical/spherical KdV equation has been investigated by using the simplified homogeneous balance method. It has been proven that if its coefficients satisfy certain constraint conditions, then the cylindrical/spherical KdV equation has a nonlinear transformation that converts the solution of the quadratic form equation into the solution of the cylindrical/spherical KdV equation. The quadratic form equation admits a series of solutions expressed by the exponential functions, therefore one soliton-like solution and multi soliton-like solutions of the cylindrical/spherical KdV equation can be obtained exactly.

Keywords: variable coefficient cylindrical/spherical KdV equation; nonlinear transformation; quadratic form equation; soliton-like solution; multi soliton-like solution; simplified homogeneous balance method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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