Rational solutions for the nonlocal sixth-order nonlinear Schrödinger equation. (English) Zbl 1538.35346
Summary: We derive the nonlocal sixth-order nonlinear Schrödinger (NLS) equation which admits rational solutions. Through the Lax pair, we prove the integrability of the nonlocal NLS equation. Furthermore, with the Darboux transformation, analytic rational solutions up to the second order are explicitly given.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35C08 | Soliton solutions |
| 35C05 | Solutions to PDEs in closed form |
Keywords:
nonlocal nonlinear Schrödinger equations; Lax pair; Darboux transformation; rational solutionsReferences:
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