Dynamics of Jacobi elliptic and soliton solutions for the modified quadratic-cubic nonlinear Schrödinger equation

ABSTRACT

We consider the quadratic-cubic nonlinear Schrödinger equation in the presence of external source, as an approximate model for a relatively quasi-1D Bose-Einstein condensate coupled to a waveguide. A scaling transformation is used to obtain a wide class of exact solutions for this model. It possesses fractional transform Jacobi elliptic solutions whose dynamics can be controlled by judicious choice of source and nonlinearity parameters. For other parametric conditions, this model exhibits bright/dark, Lorentzian-type and rational dark solitons. The presence of quadratic nonlinear term introduces a constant background and thus amplified the propagating wave. Further, the phase of the propagating wave is locked to the source and can be made either in- or out of-phase to the source wave through sign reversal of source parameter.

Keywords:

• Nonlinear optics
• quadratic-cubic nonlinear Schrödinger equation
• solitons

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

A.G. gratefully acknowledges Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India for the award of SERB Start-Up Research Grant (Young Scientists) (Sanction No: YSS/2015/001803). H.K. is thankful to SERB-DST, India for the award of fellowship.