The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism

The generalized Sinh-Gordon potential is solved within quantum Hamiltonian Jacobi approach in the framework of PT symmetry. The quasi exact solutions of energy eigenvalues and eigenfunctions of the generalized Sinh-Gordon potential are found for n=0,1 states.Comment: 10 pages appear to in IJT

Exact form factors for the scaling Z{N}-Ising and the affine A{N-1}-Toda quantum field theories

Previous results on form factors for the scaling Ising and the sinh-Gordon models are extended to general $Z_{N}$-Ising and affine $A_{N-1}$-Toda quantum field theories. In particular result for order, disorder parameters and para-fermi fields $\sigma_{Q}(x), \mu_{\tilde{Q}}(x)$ and $\psi_{Q}(x)$ are presented for the $Z_{N}$-model. For the $A_{N-1}$-Toda model all form factors for exponentials of the Toda fields are proposed. The quantum field equation of motion is proved and the mass and wave function renormalization are calculated exactly.Comment: Latex, 11 page

An application of the Casoratian technique to the 2D Toda lattice equation

A general Casoratian formulation is proposed for the 2D Toda lattice equation, which involves coupled eigenfunction systems. Various Casoratian type solutions are generated, through solving the resulting linear conditions and using a Baecklund transformation.Comment: 11 page

Baxter equations and Deformation of Abelian Differentials

In this paper the proofs are given of important properties of deformed Abelian differentials introduced earlier in connection with quantum integrable systems. The starting point of the construction is Baxter equation. In particular, we prove Riemann bilinear relation. Duality plays important role in our consideration. Classical limit is considered in details.Comment: 28 pages, 1 figur

Some New Exact Solutions of Jacobian Elliptic Functions in Nonlinear Physics Problem

Abstract:An extended mapping method with symbolic computation is developed to obtain some new periodic wave solutions in terms of Jacobin elliptic function for nonlinear elastic rod equation arising in physics.As a result,many exact travelling wave solutions are obtained which include Jacobian elliptic functions solutions,combined Jacobian elliptic functions solutions and triangular function solutions.Solutions in the limiting cases have also been studied.It is shown that the mapping method provides a very effective and powerful mathematical tool for solving nonlinear evolution equations in physics