Analytical construction of soliton families in one- and two-dimensional nonlinear Schrodinger equations with nonparity-time-symmetric complex potentials

The existence of soliton families in nonparity-time-symmetric complex potentials remains poorly understood, especially in two spatial dimensions. In this article, we analytically investigate the bifurcation of soliton families from linear modes in one- and two-dimensional nonlinear Schrodinger equations with localized Wadati-type nonparity-time-symmetric complex potentials. By utilizing the conservation law of the underlying non-Hamiltonian wave system, we convert the complex soliton equation into a new real system. For this new real system, we perturbatively construct a continuous family of low-amplitude solitons bifurcating from a linear eigenmode to all orders of the small soliton amplitude. Hence, the emergence of soliton families in these nonparity-time-symmetric complex potentials is analytically explained. We also compare these analytically constructed soliton solutions with high-accuracy numerical solutions in both one and two dimensions, and the asymptotic accuracy of these perturbation solutions is confirmed.

Automated summary

This article analytically investigates the emergence of soliton families in non-parity-time-symmetric complex potentials in two spatial dimensions, by converting the complex soliton equation into a real system and perturbatively constructing a continuous family of solitons bifurcating from linear eigenmodes. The accuracy of these perturbation solutions is confirmed through comparison with high-accuracy numerical solutions.