Some exact Solutions of the Korteweg-de Vries Equation with Variable Coefficients
Zbornik radova, Tome 4 (1984) no. 12, p. 61
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A solution in the form of separated variables of the type of similarity solutions of the classical Korteweg-de Vries equation, a solution in the form of a solitary wave moving in a time-dependent and nonuniform background and a solution in the form of a solitary wave of constant length for the Korteweg-de Vires equation with variable coefficients are found to exist by means of suitable transformations of variables and are discussed in the paper.