Existence of Formal Conservation Laws of a Variable-Coefficient Korteweg--de Vries Equation from Fluid Dynamics and Plasma Physics via Symbolic Computation

Employing the method which can be used to demonstrate the infinite conservation laws for the standard Korteweg--de Vries (KdV) equation, we prove that the variable-coefficient KdV equation under the Painleve test
condition also possesses the formal conservation laws.