In this paper classical solutions of the degenerate fifth Painlev\'e equation are classified, which include hierarchies algebraic and expressible in terms Bessel functions. Solutions known to third equation. Two applications these discussed, deriving exact complex sine-Gordon coefficients three-term recurrence relation associated with generalised Charlier polynomials.

Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and ‘‘chaos cascade’’ referring to the embeddings of smaller scale chaos in larger scale chaos. 2003 Elsevier Ltd. All rights reserved.

This paper explores the utility of a discrete singular convolution (DSC) algorithm for the integration of the sine-Gordon equation. The initial values are chosen close to a homoclinic manifold for which previous methods have encountered significant numerical difficulties such as numerically induced spatial and temporal chaos. A number of new initial values are considered, including a case where...

Fred Cooper, 2, ∗ Pasquale Sodano, † Andrea Trombettoni, ‡ and Alan Chodos § T-8, Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos NM 87545 National Science Foundation, Arlington, VA 22230 3 Dipartimento di Fisica e Sezione I.N.F.N., Universita di Perugia ,Via A. Pascoli I-06123, Perugia, Italy. 4 Dipartimento di Fisica e Sezione I.N.F.N., Universita di Perugia, Via A. ...

The edge state theory of a class of symmetric double-layer quantum Hall systems with interlayer electron tunneling reduces to the sum of a free field theory and a field theory of a chiral Bose field with a self-interaction of the sine-Gordon form. We argue that the perturbative renormalization group flow of this chiral sine-Gordon theory is distinct from the standard (non-chiral) sine-Gordon th...

As 71 is varied over the range ~ < ~/< ~c, this potential exhibits a variety of structures. Although in later sections we shall discuss these different structures in some detail [2], it is important here to provide a qualitative feeling for them. Clearly, for ~ _+ oo, 'V(~) reduces to a sine-Gordon [SG] form for q~, while for 71 = 0, it leads to a SG form for q~/2. Thus in both these limits the...

We consider an integrable generalization of the sine-Gordon (sG) equation that was earlier derived by one of the authors using bi-Hamiltonian methods. This equation is related to the sG equation in the same way that the Camassa-Holm equation is related to the KdV equation. In this paper we: (a) Derive a Lax pair. (b) Use the Lax pair to solve the initial value problem on the line. (c) Analyze s...

In this paper we consider the initial value problem for the sineGordon equation by using the homotopy perturbation method. The advantage of this method that is its ability and flexibility to provide the analytical or approximate solutions to linear and nonlinear equations without linearization or discretization makes it reliable for solving the sine-Gordon equation. The numerical results are pr...