Controllable rogue wave and mixed interaction solutions for the coupled Ablowitz-Ladik equations with branched dispersion. (English) Zbl 1476.35083
Summary: Under consideration are the coupled Ablowitz-Ladik lattice equations with branched dispersion, which may be used to model the propagation of an optical field in a tight binding waveguide array. The discrete generalized \(( m , N - m )\)-fold Darboux transformation based on \(2 \times 2\) Lax pair is extended to construct rogue wave solutions for this discrete coupled system with \(4 \times 4\) Lax pair. Novel position controllable rogue wave with multi peaks and depressions and mixed interaction structures of breather and rouge wave are shown graphically. It is clearly shown that these new discrete rogue wave structures in this coupled system are different from those of the single component Ablowitz-Ladik equation. These results may be useful to explain some physical phenomena in nonlinear optics.
MSC:
| 35C08 | Soliton solutions |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
Keywords:
discrete generalized \(( m, N - m )\)-fold Darboux transformation; controllable rogue wave; mixed interaction solutionReferences:
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