Stability of traveling wave solutions of the generalizedKorteweg-de-Vries equation

摘要

The eigenvalue problems arise in the analysis of stability of travelingwave solutions are currently dealt with, using the Evans method. It had beenshown in the literature that use of this method is not straightforward even in verysimple examples. A straightforward approach by using canonical transformationsand invariance of geometrical structure of solutions under small disturbances ispresented. Attention is focused to find exact eigenvalue and eigenfunction solutionsof the generalized Korteweg-de-Vries equation.