Nonlinear tunnelling effect of combined Kuznetsov–Ma soliton in (3+1)-dimensional $${{\varvec{\mathcal {PT}}}}$$ PT -symmetric inhomogeneous nonlinear couplers with gain and loss

Abstract

A (3+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation in parity-time symmetric inhomogeneous nonlinear couplers with gain and loss is studied, and the PT -symmetric and PT -antisymmetric combined Kuznetsov-Ma soliton solutions are obtained via the Darboux transformation method. Nonlinear tunnelling effect of controllable combined Kuznetsov-Ma solitons such as their restraint, maintenance and postpone are discussed when they pass through the dispersion/diffraction barrier and well.

Model of compact 3D electromagnetic solitons

“…The nonlinearity in bulk media usually rouses collapsing or fragmentation phenomena, so the creation of three-dimensional solitons is a challenging problem. Nevertheless, multidimensional solitons were predicted in nonlinear optics [4], ferromagnetics [5][6][7][8][9], superconductors [10], Bose-Einstein condensates [11], field theory [12], nonlinear couplers [13] and nonlinear long waves [14]. Among the nonlinear equation, the nonlinear Schrödinger equation (NSE) is very important soliton equation which is widely used for description the evolution of the optical pulses and surface gravity waves [15,16].…”

Hollow ring-like soliton and dipole soliton in ( $$\varvec{2+1}$$ 2 + 1 )-dimensional $$\varvec{\mathcal {PT}}$$ PT -symmetric nonlinear couplers with gain and loss

“…Since Christodoulides and co-workers [13] did the pioneering theoretical research about the PT symmetry in optics, soliton dynamics in PT -symmetric potentials were intensively studied [7,8,[14][15][16]. Moreover, dynamical properties of solitons in PT -symmetric nonlinear couplers were also extensively discussed [17][18][19]. However, the completely localized structures in x and y directions were hardly reported in (2 + 1)-dimensional PT -symmetric coupled systems.…”