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

• Published in: Mathematics (Basel) Vol. 10; no. 17; p. 3117
• Main Authors: Li, Lingxiao, Wang, Mingliang
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.08.2022
• Subjects: Acoustics; Coefficients; Conflicts of interest; Differential equations, Partial; Exponential functions; Geometry; Investigations; Mathematical research; multi soliton-like solution; nonlinear transformation; Quadratic equations; quadratic form equation; Quadratic forms; simplified homogeneous balance method; Solitary waves; soliton-like solution; variable coefficient cylindrical/spherical KdV equation; United States
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10173117

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.