Journal
NONLINEARITY
Volume 31, Issue 12, Pages 5385-5409Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6544/aae031
Keywords
nonlocal nonlinear Schrodiinger equation; Hirota's bilinear method; the KP hierarchy reduction method; soliton solutions with zero and nonzero boundary conditions
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Funding
- NSF [DMS-1712793, DMS-1715991]
- NSF of China [11728103]
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General soliton solutions to a nonlocal nonlinear Schrodinger (NLS) equation with PT-symmetry for both zero and nonzero boundary conditions are considered via the combination of Hirota's bilinear method and the Kadomtsev-Petviashvili (KP) hierarchy reduction method. First, general N-soliton solutions with zero boundary conditions are constructed. Starting from the tau functions of the two-component KP hierarchy, it is shown that they can be expressed in terms of either Gramian or double Wronskian determinants. On the contrary, from the tau functions of single component KP hierarchy, general soliton solutions to the nonlocal NLS equation with nonzero boundary conditions are obtained. All possible soliton solutions to nonlocal NLS with Parity (PT)-symmetry for both zero and nonzero boundary conditions are found in the present paper.
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