TY  - JOUR
AU  - Afzal, Muhammad
AU  - Ismaeel, Tariq
AU  - Butt, Azhar Iqbal Kashif
AU  - Farooq, Zahid
AU  - Ahmad, Riaz
AU  - Khan, Ilyas
PY  - 2023
TI  - On the reducibility of a class of almost-periodic linear Hamiltonian systems and its application in Schrödinger equation
JO  - AIMS Mathematics
SP  - 7471
EP  - 7489
VL  - 8
IS  - 3
AB  - In the present paper, we focus on the reducibility of an almost-periodic linear Hamiltonian system               d      X              d      t        =  J  [  A  +  ε  Q  (  t  )  ]  X  ,  X  ∈            R              2      d        ,where    J is an anti-symmetric symplectic matrix,    A is a symmetric matrix,    Q  (  t  ) is an analytic almost-periodic matrix with respect to    t, and    ε is a parameter which is sufficiently small. Using some non-resonant and non-degeneracy conditions, rapidly convergent methods prove that, for most sufficiently small    ε, the Hamiltonian system is reducible to a constant coefficients Hamiltonian system through an almost-periodic symplectic transformation with similar frequencies as    Q  (  t  ). At the end, an application to Schrödinger equation is given.
UR  - https://doi.org/10.3934/math.2023375
DO  - 10.3934/math.2023375