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Analytical construction of soliton families in one‐ and two‐dimensional nonlinear Schrödinger equations with nonparity‐time‐symmetric complex potentials
Author(s) -
Yang Jianke
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12383
Subject(s) - soliton , nonlinear system , hamiltonian (control theory) , amplitude , bifurcation , perturbation (astronomy) , physics , perturbation theory (quantum mechanics) , conservation law , mathematical physics , numerical analysis , mathematics , classical mechanics , mathematical analysis , quantum mechanics , mathematical optimization
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.