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Highly dispersive optical solitons in polarization-preserving fibers with Kerr law nonlinearity by Lie symmetry. (English) Zbl 1479.78023

Summary: The concept of highly dispersive (HD) optical solitons was first introduced during 2019 and has become extremely popular and has gained a lot of attention in the fibre optics community. We will study the problem with the aid of Lie symmetry analysis which is a very powerful mathematical scheme to handle differential equations that typically arise in nonlinear physics.

MSC:

78A60 Lasers, masers, optical bistability, nonlinear optics
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q41 Time-dependent Schrödinger equations and Dirac equations
35B06 Symmetries, invariants, etc. in context of PDEs
35C08 Soliton solutions
37L50 Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems
22E70 Applications of Lie groups to the sciences; explicit representations
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