Supratim Das

Nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator

We examine some nontrivial consequences that emerge from interpreting a position-dependent mass (PDM)-driven Duffing oscillator in the presence of a quartic potential. The propagation dynamics is numerically studied and the sensitivity to the PDM-index is noted. Remarkable transitions from a limit cycle to chaos through period doubling and from a chaotic to a regular motion through intermediate periodic and chaotic routes are demonstrated.

New exact solutions of a generalized shallow water wave equation

In this work, an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate on how to classify new exact travelling wave solutions expressible in terms of quasi-periodic elliptic integral functions and doubly periodic Jacobian elliptic functions. The derived new solutions include rational, periodic, singular and solitary wave solutions. An interesting comparison with the canonical procedure is provided. In some cases the obtained elliptic solution has singularity at a certain region in the whole space. For such solutions we have computed the effective region where the obtained solution is free from such a singularity.

Reply to Comment on ‘Nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator’

In response to the comment of Mustafa (2013 J. Phys. A: Math. Theor. 46 368001) we justify our stand of considering an extended Lagrange equation involving a non-conservative force term when the particle mass varies with position. As has been known for some time, such an extended form not only takes into account the principle of virtual work applied to D’Alembert’s principle but yields precisely the form of Newton’s equation expected for a particle possessing a position-dependent mass.