We propose amodel of a kink bearing Hamiltonianwith a new non-linear potential V ( q , p ) whose double-well shape can be vaned continuously as a function of the parameter p and which has the q 4 potential as a particular case. Exact classical kink solutions that dependonp areobtained. The rest masses and restenergiesof the kinksare also determined, In recent years non-linear monatomic chain models have been extensively used in condensed-matter physics because they provide a non-perturbation approach to strongly anharmonic systems. The governing equations frequently admit large-amplitude localized field profiles that are physically distinct from those obtainable by superposition of small-amplitude or linearized profiles. These localized large-amplitude excitations canpropagate through thesystem without distortionofshaFeandarecommonly referred to as solitary waves. They exhibit remarkable stability and other particle-like properties.Because of their localized nature, they have found widespread use as one-dimensional models of extended particles in non-linear quantum-field theories, dislocations in crystals, planar domain walls in ferromagnets and ferroelectrics, propagatingflux quanta in Josephson transmission lines, disgyration planes in superfluid He, charge carriers in weakly pinned charge-density-wavecondensates, and charged dislocations in superionic conductors, to mention only a few examples.Various kinds of non-linear potential have been proposed to explain these phenomena. As examples, we may retain the Toda potential (1967), the Lennard-Jones potential, the Morse potential, the sineGordon and double sine-Gordon potentials, the q4, @and @fields, adouble quadratic potential, the Schmidt potential (1979), the Magyari potential (1981), the Behera and Khare potential (1981) and the Remoissenet-Peyrardpotential(l981).Consider a general class of non-linear solitary wave bearing one-dimensional lattice Hamiltonians (see Currie er al1980).where pi is a one-component dimensionless field defined on a one-dimensional lattice of points with lattice constant 1. The first term represents the kinetic energy carried by the field, the second represents harmonic coupling between field values at neighbouring

A two-loop soliton solution to the Schäfer-Wayne short-pulse equation (SWSPE) is shown. The key step in finding this solution is to transform the independent variables in the equation. This leads to a transformed equation for which it is straightforward to find an explicit two-soliton solution using Hirota's method. The two-loop soliton solution to the SWSPE is then found in implicit form by means of a transformation back to the original independent variables. Following Hodnett and Moloney's approach, some computations of the energy of the one-and two-soliton solutions are made.

No abstract

We study the nonlinear dynamics of the DNA double-helical chain using the Peyrard-Bishop-Dauxois (PBD) model. By using the Fourier series approach, we have found that the DNA dynamics in this case is governed by the modified discrete nonlinear Schrödinger (MDNLS) equation. Through the Jacobian elliptic function method, we investigate a set of exact solutions of this model. These solutions include the Jacobian periodic solution as well as bubble solitons. The stability of these solutions is also studied.