Soliton solution in nonlinear lattice with nearest neighbour Born–Mayer interaction

Abstract

We study the dynamics of one-dimensional uniform lattice with the interatomic Born-Mayer potential. The travelling wave solutions such as solitons are analytically described. The wave propagation in the one-dimensional lattice where nearest neighbour atoms interact via the Born-Mayer potential is considered. The Born-Mayer lattice admits travelling wave type solutions represented by Jacobian elliptic functions and limiting form of such a wave solution is the localized pulse-like form called the solitary wave. This solitary wave has further remarkable properties under collision, leading to the concept of solitons in nonlinear discrete lattices which has been studied.

Phase Space Analysis and Soliton Solution for Quartic Potential

“…We have studied the concept of anharmonicself localized modes in much wider areas in one-dimensional lattice as compared with the previous studies, where only the quartic anharmonicity was taken care of [18,19,20,21,23]. The theory was formulated by making extensive use of the Lattice-Green's function method which provides us with a natural theoretical basis of studying the localization properties of anharmonic vibrations and for justifying the use of the so called rotating wave approximation RWA.…”

Dynamics of solitons in nonlinear lattices with Morse potential

“…This equation of motion (18) reduces to the Born-Mayer lattice equation [15] for small momentum for the negative root, and for the positive root the equation of motion becomes…”

“…So far much of the work has been done either numerically or involves approximating the potentials by a Toda potential with parameters satisfying appropriate conditions for various problems. We follow up on earlier work [13][14][15][16][17] with generalized addition theorems for Jacobian Elliptic Functions (JEF) dn(u,k), where k denotes the modulus of the elliptic functions to obtain solutions for these nonlinear excitations.…”