Ndogmo. Jean-ClaudeFolly-Gbetoula, MensahMbala, Emmanuel Mayombo2026-06-172026-06-172026-05-19Mbala, E.M. 2026. Lie group analysis of Schr¨odinger equations describing optical waves in birefringent waveguides. . .https://univendspace.univen.ac.za/handle/11602/3205M.Sc. in MathematicsDepartment of Mathematical and Computational SciencesLie group analysis will be carried out for a system of two nonlinear Schr¨odinger equations characterizing the propagation of optical pulses and involving fourwave mixing terms in a birefringent media. The ultimate goal is to find the most general symmetry transformation that preserves the solution space and generates in particular a series of solutions of the system starting from a seed solution. Such a general symmetry transformation is the symmetry group, and it will be computed from the symmetry algebra L of the system rewritten as a system of four nonlinear uncoupled equations in real form. An optimal system of one dimensional subalgebras of L will be found and some related symmetry reductions will be given. Soliton or other solutions will be obtained by means of either the Hirota direct method, or some substitution methods such as the Tanh-expansion method or its variants else by other common methods including the direct Lie group methods.1 online resource (vi, 58 leaves)enUniversity of VendaSymmetry groupUCTDSolution transformationsOptimal system of subalgebrasSymmetry reductionsSoliton solutionsThesisMbala EM. Lie group analysis of Schr¨odinger equations describing optical waves in birefringent waveguides. []. , 2026 [cited yyyy month dd]. Available from:Mbala, E. M. (2026). <i>Lie group analysis of Schr¨odinger equations describing optical waves in birefringent waveguides</i>. (). . Retrieved fromMbala, Emmanuel Mayombo. <i>"Lie group analysis of Schr¨odinger equations describing optical waves in birefringent waveguides."</i> ., , 2026.TY - Thesis AU - Mbala, Emmanuel Mayombo AB - Lie group analysis will be carried out for a system of two nonlinear Schr¨odinger equations characterizing the propagation of optical pulses and involving fourwave mixing terms in a birefringent media. The ultimate goal is to find the most general symmetry transformation that preserves the solution space and generates in particular a series of solutions of the system starting from a seed solution. Such a general symmetry transformation is the symmetry group, and it will be computed from the symmetry algebra L of the system rewritten as a system of four nonlinear uncoupled equations in real form. An optimal system of one dimensional subalgebras of L will be found and some related symmetry reductions will be given. Soliton or other solutions will be obtained by means of either the Hirota direct method, or some substitution methods such as the Tanh-expansion method or its variants else by other common methods including the direct Lie group methods. DA - 2026-05-19 DB - ResearchSpace DP - Univen KW - Symmetry group KW - Solution transformations KW - Optimal system of subalgebras KW - Symmetry reductions KW - Soliton solutions LK - https://univendspace.univen.ac.za PY - 2026 T1 - Lie group analysis of Schr¨odinger equations describing optical waves in birefringent waveguides TI - Lie group analysis of Schr¨odinger equations describing optical waves in birefringent waveguides UR - ER -