Conditional Similarity Reductions of Jimbo-Miwa Equation via the Classical Lie Group Approach**The project supported by the National Outstanding Youth Foundation of China (No. 19925522) and the Research Fund for the Doctoral Program of Higher Education of China (Grant. No. 2000024832)

Abstract

Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo–Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.