Dbar‐approach to coupled nonlocal NLS equation and general nonlocal reduction
Copyright policy )Dbar‐approach to coupled nonlocal NLS equation and general nonlocal reduction
AbstractThe coupled nonlocal nonlinear Schrödinger (NLS) equation is studied by virtue of the Dbar‐problem. Two spectral transform matrices are introduced to define two associated Dbar‐problems. The relations between the coupled nonlocal NLS potential and the solution of the Dbar‐problem are constructed. The spatial transform method is extended to obtain the coupled nonlocal NLS equation and its conservation laws. The general nonlocal reduction of the coupled nonlocal NLS equation to the nonlocal NLS equation is discussed in detail. The explicit solutions are derived.
- Zhengzhou University China (People's Republic of)
Nonlinear Sciences - Exactly Solvable and Integrable Systems, NLS equations (nonlinear Schrödinger equations), FOS: Physical sciences, Analyticity in context of PDEs, Solutions to PDEs in closed form, nonlocal NLS equation, Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, general nonlocal reduction, Time-dependent Schrödinger equations and Dirac equations, Dbar-problem, Riemann-Hilbert problems in context of PDEs, Exactly Solvable and Integrable Systems (nlin.SI), dressing method
Nonlinear Sciences - Exactly Solvable and Integrable Systems, NLS equations (nonlinear Schrödinger equations), FOS: Physical sciences, Analyticity in context of PDEs, Solutions to PDEs in closed form, nonlocal NLS equation, Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, general nonlocal reduction, Time-dependent Schrödinger equations and Dirac equations, Dbar-problem, Riemann-Hilbert problems in context of PDEs, Exactly Solvable and Integrable Systems (nlin.SI), dressing method
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