<scp>KAM</scp>Theorem with Normal Frequencies of Finite<scp>Limit‐Points</scp>for Some Shallow Water Equations
Xiaoping Yuan
Abstract
By constructing an infinite‐dimensional KAM theorem of the normal frequencies being dense at a finite point, we show that some shallow water equations such as the Benjamin‐Bona‐Mahony equation and the generalized d ‐dimensional Pochhammer‐Chree equation subject to some boundary conditions possess many (a family of initial values of positive Lebesgue measure of finite dimension) smooth solutions that are quasi‐periodic in time . © 2020 Wiley Periodicals LLC
Topics & Concepts
MathematicsKolmogorov–Arnold–Moser theoremLimit (mathematics)Mathematical analysisLebesgue measureDimension (graph theory)Lebesgue integrationWaves and shallow waterPure mathematicsIntegrable systemPhysicsThermodynamicsQuantum chaos and dynamical systemsNonlinear Waves and SolitonsNumerical methods for differential equations