Asymptotics of Ndimensional tori in the generalized Korteweg  de Vries equation
Abstract
We consider the generalized Korteweg  de Vries (KdV) equation with periodic boundary condition by space variable. The asymptotics of periodic solutions and invariant tori are considered in a sufficiently small neighbourhood of the zero equilibrium state. There are considered two cases: the coefficient of the quadratic term in the right part of generalized KdV equation is nonzero or zero. In the first case, the cycles and twodimension tori are unstable. In the second, case it is proved that cycles are stable and tori are unstable.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 January 2018
 DOI:
 10.1088/17426596/955/1/012022
 Bibcode:
 2018JPhCS.955a2022G