A focusing and defocusing semi-discrete complex short pulse equation and its varioius soliton solutions
arXiv:1901.02388
Abstract
In this paper, we are concerned with a a semi-discrete complex short pulse (CSP) equation of both focusing and defocusing types, which can be viewed as an analogue to the Ablowitz-Ladik (AL) lattice in the ultra-short pulse regime. By using a generalized Darboux transformation method, various solutions to this newly integrable semi-discrete equation are studied with both zero and nonzero boundary conditions. To be specific, for the focusing CSP equation, the multi-bright solution (zero boundary condition), multi-breather and high-order rogue wave solutions (nonzero boudanry conditions) are derived, while for the defocusing CSP equation with nonzero boundary condition, the multi-dark soliton solution is constructed. We further show that, in the continuous limit, all the solutions obtained converge to the ones for its original CSP equation (see Physica D, 327 13-29 and Phys. Rev. E 93 052227)
arXiv comment20 pages, 4 figures
References in corpus (8)
- Theory of Bose-Einstein condensation in trapped gases
- Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
- The short pulse equation is integrable
- Complex short pulse and coupled complex short pulse equations
- General rogue waves in the focusing and defocusing Ablowitz-Ladik equations
- Integrable discretizations of the short pulse equation
- A defocusing complex short pulse equation and its multi-dark soliton solution by Darboux transformation
- Casorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation