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.
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