ON THE BI-HAMILTONIAN STRUCTURE, STRONG AND HEREDITARY OPERATOR OF SYMMETRIES FOR A NEW NONLINEAR-SYSTEM

The bi-Hamiltonian structure, strong, and hereditary operator for symmetries for a new nonlinear integrable system have been deduced by the procedure of Fourier analysis and small amplitude expansion. The recursion operator for the gradient of conserved quantities has been written down. An important feature of this approach is that, it is possible to obtain several solutions of the equation determining the symplectic operator. But unfortunately one cannot construct the strong (hereditary) operator from all such pairs of solution. Only for some special solutions it was possible to do so. In these cases the strong and hereditary property can be proven explicitly. In the following, examples of operators belonging to both of these classes will be cited.