Self-localized modes in a quantum vibronic system, with long range interaction of Kac-Baker type and interacting nonlinearly with an acoustical phonon bath, is studied. One works in the coherent state approximation. Following a procedure of Sarker and Krumhansl the problem is reduced to a nearest neighbours one. In the continuum limit the localized state satisfy a mKdV equation. An approximate ...

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of nonlinear evolution equations with variable coefficients. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, new explicit solutions including solitary wave solutions and trigonometric function solutions...

We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which inc...

Abstract: In this paper, the Exp-function method with the aid of symbolic computational system is used to obtain generalized solitary solutions and periodic solutions of the MKdV equation, Burgers’ equation in one and two dimensional with variable coefficients. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving othe...