The approximate manifolds for the generalized (2+1)-dimensional long-short wave equations (Q766214)

The authors consider a class of dissipative generalized (2+1)-dimensional long-short wave resonance interaction equations. They show that solutions exist globally in time and remain bounded in some Sobolev space if appropriate conditions on the initial conditions and the growth of nonlinearities are assumed. Using the projection method they are also able to prove the existence of an approximate inertial manifold, i.e. a finite-dimensional manifold that possesses a small neighborhood which attracts all solutions.