İrma Hacınlıyan (Istanbul Technical University)

Title: On Nonlinear Schrödinger Type Equations: Wave Modulation and Mathematical Analysis

Abstract: The nonlinear Schrödinger (NLS) equation describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear dispersive media. The NLS equation with soliton solutions is one of the significant and widely pursued research areas on the nonlinear wave motions. Sub-studies on such evolution equations include derivations of those equations; finding exact solutions and developing methods for these; studies of the analytic and geometric structure of the equations as integrable systems; singularities and collapses of solutions; analyzing modulation equations by dynamical systems methods; and related subjects. In this talk, nonlinear modulation of waves propagating in a generalized elastic solid according to different physical scenarios will be discussed. Properties of the solutions of NLS-type equations that are derived using the reductive perturbation method will be examined by mathematical analysis methods.