Abstract: The inverse scattering formalism provides a general scheme for solving the integrable nonlinear partial differential equations. Indeed, many interesting solutions have been obtained by means of different implementations of this strategy. In the periodic case, this approach does not provide much help in finding explicit (at least approximate) solutions of the initial value problems for arbitrarily chosen initial conditions. In the talk, we shall address some issues related to this problem by means of a perturbative approach. Linear Fourier theory, and more generally the Sturm-Liouville theory, provide the tool for constructing the solutions of certain linear partial differential equations in the form of the linear superposition of elementary Fourier modes. The inverse scattering method can be viewed as a nonlinear relative of the Fourier analysis. In the talk, method of constructing nonlinear Fourier modes will be proposed. In perspective, a suitable nonlinear superposition principle of these nonlinear modes will enable us to solve initial problems with arbitrary initial conditions.
Seminarsko predavanje (v angleškem jeziku) bo v četrtek 24. novembra 2016 ob 15:15 uri v seminarski sobi CAMTP na Mladinski 3, drugo nadstropje levo. Vljudno vabljeni vsi zainteresirani, tudi študentje.