Symmetry broken and unbroken solutions of nonlocal NLS equation in 2+1 dimensions

• Published in: Results in physics 2020-06, Vol.17, p.103100, Article 103100
• Main Authors: Sarfraz, H., Saleem, U.
• Format: Article
• Language: English
• Subjects: Darboux transformation (DT); Quasideterminants; Reverse space nonlocal nonlinear Schrödinger (NLS) equation in 2+1 dimensions; Reverse space nonlocal nonlinear Schrödinger (NLS) equation in [formula omitted] dimensions; Symmetry unbroken and broken solutions
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2020.103100

•A generalized nonlinear Schrödinger (NLS) equation in 2+1 dimensions is considered.•Reverse space nonlocal NLS equation is deduced from a generic one by applying suitable nonlocal symmetry reduction.•Darboux transformation is applied to construct nontrivial solutions. The results are expressed in quasideterminant representation.•Both symmetry broken and symmetry unbroken first two nontrivial solutions are computed.•Unstable (line & parabolic) solitons, oscillating singular-type solutions and stable soliton solutions are obtained for 2+1-dimensional general, nonlocal & local NLS equations. In this paper, we study a general nonlinear Schrödinger (NLS) equation in 2+1 dimensions which under appropriate nonlocal symmetry reduction leads to reverse space nonlocal NLS equation. We apply Darboux transformation and construct multiple solutions of NLS equation in 2+1 dimensions which are expressed in terms of quasideterminants. Under suitable reductions the quasideterminant formula empowers us to compute explicit expressions of symmetry broken and symmetry unbroken solutions of a generic NLS equation and PT-symmetric reverse space nonlocal NLS equation in 2+1 dimensions respectively. Furthermore the dynamics of symmetry broken and symmetry unbroken first two nontrivial solutions are presented. Under the dimensional reduction we obtain first- and second-order nontrivial solutions of 1+1-dimensional nonlocal NLS equation. By applying local symmetry reduction, we obtain one- and two-soliton solutions of 2+1-dimensional local NLS equation.