arXiv subjects
Publications and source records attributed to Jen-Hsu Chang.
We investigate the reductions of dispersionless Harry Dym hierarchy to systems of finitely many partial differential equations. These equations must satisfy the compatibility condition and they are diagonalizable and semi-Hamiltonian. By imposing a further constraint, the compatibility is reduced to a system of algebraic equations, whose solutions are described.
We deform the Dorfman's and Sokolov's Hamiltonian operators by the quasi-Miura transformation coming from the topological field theory and investigate the deformed operators.
We construct one-parameter deformation of the Dorfman Hamiltonian operator for the Riemann hierarchy using the quasi-Miura transformation from topological field theory. In this way, one can get the approximately rational symmetries of KdV equation and then investigate its bi-Hamiltonian structure.
The integrability of the generalized Benney hierarchy with three primary fields is investigated from the point of view of two-dimensional topological field theories coupled to gravity. The associated primary free energy and correlation functions at genus zero are obtained via Landau-Ginzburg formulation and the string equation is derived using the twistor construction for the Orlov operators. By adopting the approach of Dubrovin and Zhang we obtain the genus-one corrections of the Poisson brackets of the generalized Benney hierarchy.
The bi-Hamiltonian structure of the Benney hierarchy is revisited. We show that the compatibility condition of the Poisson brackets provides the genus zero free energy of a topological field theory coupled to 2d gravity. We calculate the correlation functions via the Landau-Ginzburg formulation and derive the string equation based on the twistor construction. Moreover, by using the approach of Dubrovin and Zhang, we compute the genus one correction of the Poisson brackets and compare them with the Oevel-Strampp's brackets of the Kaup-Broer hierarchy.
We investigate the bi-Hamiltonian structures associated with constrained dispersionless modified KP hierarchies which are constructed from truncations of the Lax operator of the dispersionless modified KP hierarchy. After transforming their second Hamiltonian structures to those of Gelfand-Dickey type, we obtain the Poisson algebras of the coefficient functions of the truncated Lax operators. Then we study the conformal property and free-field realizations of these Poisson algebras. Some examples are worked out explicitly to illustrate the obtained results.
We investigate the Miura map between the dispersionless KP and dispersionless modified KP hierarchies. We show that the Miura map is canonical with respect to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki and Takebe, the twistor construction of solution structure for the dispersionless modified KP hierarchy is given.