\( \bar \partial \)-dressing method for three-component coupled nonlinear Schrödinger equations. (English) Zbl 07924333
Summary: The dressing method based on \(4\times 4\) matrix \(\bar{\partial} \)-problem is extended to study the three-component coupled nonlinear Schrödinger (3DNLS) equations. The spatial and time spectral problems related to the 3DNLS equations are derived via two linear constraint equations. A 3DNLS hierarchy with source is proposed by using recursive operator. The \(N \)-solitions of the 3DNLS equations are given based on the \(\bar{\partial} \)-equation by selecting a spectral transformation matrix.
MSC:
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 35C08 | Soliton solutions |
Keywords:
three-component coupled nonlinear Schrödinger equations; \( \bar{\partial} \)-dressing method; Lax pair; soliton solutionReferences:
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