Optimal subalgebra, conservations laws and symmetry reductions with analytical solutions using Lie symmetry analysis and geometric approach for the (1+1)-dimensional Manakov model

Abstract

In this article, the (1+1)-dimensional Manakov model has been examined for finding its exact closed form solitonic solutions with the help of symmetry generators. These symmetry generators are explored using the Lie symmetry analysis, commonly known as the classical Lie group approach and the geometric approach. In a geometric approach, the extended Harrison and Estabrook’s differential forms have been used for obtaining the infinitesimal generators of the Manakov model. As there are infinite possibilities for the linear combination of infinitesimal generators, so by using Olver’s standard approach a one-dimensional optimal system of subalgebra has been established. Additionally, the ‘new conservation theorem’ put forth by Ibragimov has been utilized in order to devise the conservation laws for the (1+1)-dimensional Manakov model. Finally, the exact closed form solutions are obtained with the help of Lie symmetries corresponding to the defined model.