Two new classes of exact solutions for the KdV equation via Backlund transformations

摘要

The Korteweg-de Vries equation which includes nonlinear and dispersive terms quadratic in the wave amplitude is considered. The exact solutions can be obtained by the AKNS class. The technique developed relies on the construction of the wave functions which are solutions of the associated AKNS system: that is. a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Backlund transformations (BTs) are employed to gent rate two new solutions from the old one.