The generalized Kupershmidt deformation for the fifth-order coupled KdV equations hierarchy
The paper belongs to the category of those aiming to generate new integrable systems from a known one through various deformations. The Kupershmidt deformation is generalized as follows: \[ u_{t_n} = B_1\left({{\delta H_{n+1}}\over{\delta u}}- \sum_1^N{{\delta\lambda_j}\over{\delta u}}\right) ;\;(B_2-\alpha_jB_1) \left({{\delta\lambda_j}\over{\delta u}}\right)=0\;,\;j=1,\ldots,N, \] where \(\delta\lambda_j/\delta u\) is the variational derivative of the eigenvalues of the associated spectral problem and \(B_1\), \(B_2\) are two standard Hamiltonian operators. From here, a kind of Hamiltonian soliton equation hierarchy is obtained, describing a 5th order coupled KdV equation.
scientific article; zbMATH DE number 5880212
scientific article