Classification of Evolution Equations Possessing Two-soliton Solutions and Lax Pairs by Direct Methods

摘要

A direct method for constructing transformations from traveling wave solutions to non-traveling wave solutions of an evolution equation, has been developed. In the case, when applying the method yields transformations from one-soliton solutions to two-soliton solutions, it may be used for construction of the many-parameter families of evolution equations possessing two-soliton solutions. Such equations may, to some extent, be considered as candidates for integrable equations. In order to separate presumably integrable equations from those families, a direct method for identifying conditions for the Lax pair existence has been developed. Some new equations admitting the Lax pairs have been identified using the method.