Complete integrability of coupled quartic anharmonic oscillators

Abstract

We complete the study of the Painleve (P) analysis and integrability of the N coupled quartic anharmonic oscillators defined by H_N=1/2 J_i=1^N p_xi²⁺ J_i=1^N A_ix_i²⁺ J_i=1^Nα_ix_i⁴ +1/2 J_i,j=1^N β_ijx_i²x_j², i≠j, by listing all the P cases [including those cases which we did not present in Lakshmanan and Sahadevan, Phys. Rev. A 31, 861 (1985)] and deriving the appropriate N involutive integrals for each one of them.