New classes of solutions for the Schwarzian Korteweg–de Vries equation in (2+1) dimensions**Partially supported by projects MTM2006-05031 from DGES and FMQ201 from Junta de Andalucía.

Abstract

We have obtained new classes of solutions for the (2+1)-dimensional Schwarzian Korteweg–de Vries equation by considering several types of reductions of a system equivalent to this equation. The first analysis is done by studying the nonclassical reductions of the system. Further reductions are attained by means of other types of symmetry reductions or by ansatz-based reductions. Most of the new classes of solutions depend on Jacobian elliptic functions and solutions of a Riemann wave equation, including the cnoidal waves solutions. The new classes of solutions can display several types of coherent structures and can exhibit the overturning or intertwining phenomena, according to the suitable selection of the functions these solutions depend on.