Analytical construction of soliton families in one‐ and two‐dimensional nonlinear Schrödinger equations with nonparity‐time‐symmetric complex potentials
Abstract
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 Schrödinger 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 08, 2021
- Source ID
- 10.1111/sapm.12383
Entities
People
- Jianke Yang
Organizations
- Air Force Office of Scientific Research
- National Science Foundation
- University of Vermont