Explicit solutions for nonlocal NLS: GBDT and algebro-geometric approaches

Abstract

We apply the GBDT version of the Bäcklund-Darboux transformation to the nonlocal NLS (focusing and defocusing cases). The matrix case is included and solutions in the form of rectangular $m_1\times m_2$ matrix functions are dealt with. The wave function is also constructed explicitly. Families of explicit examples are considered in detail. Some initial results and representations for the more complicated algebro-geometric solutions are obtained as well.

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Cited by in corpus (7)

• Long-time asymptotics for the integrable nonlocal focusing nonlinear Schrödinger equation for a family of step-like initial data
• General stationary solutions of the nonlocal nonlinear Schrödinger equation and their relevance to the PT-symmetric system
• Rational solutions of the defocusing nonlocal nonlinear Schrodinger equation: Asymptotic analysis and soliton interactions
• Curved wedges in the long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation
• Defocusing nonlocal nonlinear Schrödinger equation with step-like boundary conditions: long-time behavior for shifted initial data
• Global conservative solutions of the nonlocal NLS equation beyond blow-up
• GBDT and explicit solutions for the matrix coupled dispersionless equations (local and nonlocal cases)