Rogue Wave Solutions and Modulation Instability With Variable Coefficient and Harmonic Potential

Abstract

This article studies the propagation of rogue waves with a nonautonomous NLSE in the presence of external potential. This model is considered to be an important model for many physical phenomena in quantum mechanics and optical fiber. The obtained waves are of first and second order and are investigated using similarity transformation. The nonlinear dynamic behavior of these waves is also demonstrated with different parameter values for the magnetic and gravity fields. The results show the influence of these fields over density, width, and peak heights. Moreover, the modulation instability is also discussed.

The exact solutions of Fokas-Lenells equation based on Jacobi elliptic function expansion method

“…In nonlinear optics, many equations have been modeled to structure the propagation of optical pulses in various media [21][22][23][24][25][26][27]; the most famous equation of which is nonlinear Schrödinger equation (NLSE) [28,29]. However, the Fokas-Lenells (FL) equation (1.1) was first proposed and derived by Fokas and Lenells via the bi-Hamiltonian method, which is a generalization of the NLSE [30][31][32], iq y + αq yy + βq yt + qq * (γ q + iσ rq y ) = 0, (…”

Dispersive of propagation wave solutions to unidirectional shallow water wave Dullin–Gottwald–Holm system and modulation instability analysis

“…Therefore, NLPDEs have gained a remarkable attention in the realm of nonlinear sciences due to its wide range of usage and applications in the recent decades. The NLPDEs perform a great role in ocean engineering, plasma physics, optical fibers, physics, biology, quantum physics, fluid mechanics, geochemistry and many other scientific areas to explain the dynamical and physical processes 1‐5 . The NLPDEs explain the behaviour of waves in different fields.…”

Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic‐Quintic Nonlinearities

“…[3][4][5][6][7][8] Experimentally, it has been observed in a CS2 planar waveguide. [9] In recent years, the studies of optical solitons have attracted more and more attention, which include rogue wave, [10,11] DOI: 10.1002/andp.202000048 chirped solitons, [12,13] non-Hermitian optical systems. [14] The investigations about symmetry breaking of optical solitons have been expanded into non-Hermitian optical systems with parity-time symmetric complex potential.…”