Author(s)

Jianli Cao^*, Jingfang Han

College of Science, Henan University of Technology, Zhengzhou, China.

Finite-dimensional integrable Hamiltonian system, obtained through the nonlinearization of the 3 × 3 spectral problem associated with the Boussinesq equation, is investigated. A generating function method starting from the Lax-Moser matrix is used to give an effective way to prove the involutivity of integrals. Finite-parameter solution of the Boussinesq equation is calculated based on the commutative system of ordinary differential equations with these integrals as Hamiltonians. The problem of the third order differential operator associated with the Boussinesq Neumann system put forward by H. Flaschka in 1983 is solved.

Boussinesq Equation, Conserved Integrals, Lax-Moser Matrix

Cao, J. and Han, J. (2020) A Neumann System of the Third Order Differential Operator Associated with the Boussinesq Equation. Journal of Applied Mathematics and Physics, 8, 2861-2868. doi: 10.4236/jamp.2020.812211.