The Degasperis-Procesi equation with self-consistent sources

The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.Comment: 15 page

Bulk and interfacial properties of quadrupolar fluids

We extend Teixeira and Telo da Gama’s density-functional approach [J. Phys.: Condens. Matter 3, 111 (1991)] to study the vapor–liquid phase equilibria and planar interfacial properties of quadrupolar fluids. The density profile, surface ordering, surface polarization, and surface tension of quadrupolar fluids are evaluated. Particular attention is given to the temperature and quadrupole-strength dependence. It is found that the interfacial molecular ordering can arise entirely due to the quadrupole–quadrupole interaction. It is also found that the bulk-phase properties of the quadrupolar fluids satisfy the law of correspondence states. The reduced surface potential and surface tension can be well correlated by power laws of the scaled temperature τ ≡1-T/Tc , where Tc is the critical temperature of the fluids

Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints

The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems are completely integrable in Liouville sense by finding a full set of integrals of motion and proving their functional independence.Comment: 10 pages, in LaTeX, to be published in J. Phys. Soc. Jpn. 70 (2001

Trigonal columnar self-assembly of bent phasmid mesogens

Three compounds with a bent rod-like aromatic core and with three alkoxy chains at each end were synthesised by click reaction. The compounds form a columnar liquid crystal phase with non-centrosymmetric trigonal p31m symmetry, the columns having a 3-arm star-like cross-section

A new method to introduce additional separated variables for high-order binary constrained flows

Degrees of freedom for high-order binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices are $2N+k_0$. It is known that $N+k_0$ pairs of canonical separated variables for their separation of variables can be introduced directly via their Lax matrices. In present paper we propose a new method to introduce the additional $N$ pairs of canonical separated variables and $N$ additional separated equations. The Jacobi inversion problems for high-order binary constrained flows and for soliton equations are also established. This new method can be applied to all high-order binary constrained flows admitting $2\times 2$ Lax matrices.Comment: 34 pages, AmsTex, to be published in J. Phys.