The extended symmetry approach for studying the general Korteweg-de Vries-type equation

The extended symmetry approach is used to study thegeneral Korteweg-de Vries-type (KdV-type) equation. Severalvariable-coefficient equations are obtained. The solutions ofthese resulting equations can be constructed by the solutions oforiginal models if their solutions are well known, such as thestandard constant coefficient KdV equation and the standard compoundKdV--Burgers equation, and so on. Then any one of thesevariable-coefficient equations can be considered as an originalmodel to obtain new variable-coefficient equations whose solutionscan also be known by means of transformation relations betweensolutions of the resulting new variable-coefficient equations and theoriginal equation.