Based on the differential forms and exterior derivatives of fractional orders,Wu first presented the generalized Tu formula to construct the generalized Hamiltonian structure of the fractional soliton equation.We apply the generalized Tu formula to calculate the fractional Dirac soliton equation hierarchy and its Hamiltonian structure.The method can be generalized to the other fractional soliton hierarchy.
Based on an improved fractional sub-equation method involving Jumarie's modified Riemann-Liouville derivative, we construct analytical solutions of space-time fractional compound Kd V-Burgers equation and coupled Burgers' equations. These results not only reveal that the method is very effective and simple in studying solutions to the fractional partial differential equation, but also include some new exact solutions.
Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations.The Abel-Jacobi coordinates are introduced to straighten the flows,from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.
