arXiv subjects

Mahmood ul Hassan

Publications and source records attributed to Mahmood ul Hassan.

2 recordsLinked to original sources

arXiv2019

Integrable semi-discretization of complex and multi-component coupled dispersionless systems and their solutions

An integrable semi-discretization of complex and multi-component coupled dispersionless systems via Lax pairs is presented. A Lax pair is proposed for the complex sdCD system. We derive the Lax pair for the multi-component sdCD system through generalizing the $2 \times 2$ Lax matrices to the case of $2^{N} \times 2^{N}$ Lax matrices. A Darboux transformation (DT) is applied to the complex and multi-component sdCD systems and is used to compute soliton solutions of the systems. It is also shown that the soliton solutions of the semi-discrete systems reduce to the continuous systems by applying continuum limit.

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arXiv2019

On soliton solutions of the time-discrete generalized lattice Heisenberg magnet model

Generalized lattice Heisenberg magnet model is an integrable model exhibiting soliton solutions. The model is physically important for describing the magnon bound states (or soliton excitations) with arbitrary spin, in magnetic materials. In this paper, a time-discrete generalized lattice Heisenberg magnet (GLHM) model is investigated. By writing down the Lax pair representation of the time-discrete GLHM model, we present explicitly the underlying integrable structure like, the Darboux transformation and soliton solutions.

nlin.SI↗