W-shaped, dark and grey solitary waves in the nonlinear Schrödinger equation competing dual power-law nonlinear terms and potentials modulated in time and space

ABSTRACT

This paper explores the higher-order nonlinear Schrodinger equation with dual power-law nonlinearities and external potential that can depend on space and time coordinates. We constructed exact soliton-like solutions with arbitrary power-law nonlinearities using the similarity transformation approach. We obtained a family of soliton-like solutions: the so-called W-shaped, dark and the grey solitons. These solutions are at first, found by considering just the time modulated nonlinearities, where the frame variable $X(x,t)$ coincides with the characteristic coordinate ξ. Then the nonlinearities coefficients and potential are space–time modulated with a bounded function $X(x,t)$. In both cases, a numerical study based on appropriate choices of parameters is achieved. For a fixed absolute value of nonlinearities, we examine how different soliton profiles are influenced when increasing the power-law index n. These variations of parameters display some substantial changes in solitary wave profiles; paving the way for many applications.

Keywords:

• Solitons
• power-law nonlinearities
• optical fibre
• Bose–Einstein condensate

Disclosure statement

No potential conflict of interest was reported by the authors.