- 會議論文
NLS with Quantum Potential and the Related Reaction-Diffusion Systems
並列摘要
We review some results on nonlinear Schrödinger equations with quantum potential l and the related reaction-diffusion systems. This presentation is divided by two parts. In Part I, we will review some old results about 2 by 2 AKNS-ZS system with linear and quadratic spectral parameter and the related evolution equations and the inverse scattering method under the set-up of Beals-Coifman. For the forward problem, we will explain the D-Bar idea to get the scattering data in this set-up, which is also applicable in higher dimensional cases. We will mention the ODE system for the direct problem in this set-up. This could be solved via the estimate of L^1 norm and L^2 norm of the potentials. Here the inverse problem is formulated as a Riemann-Hilbert problem with parameters. Then, in Part II, we will make a brief report on the nonlinear Schrödinger equations with quantum potential, derivative nonlinear Schrödinger equations and the related reaction-diffusion systems, which is also related to the Broer-Kaup systems. We will discuss some possible applications (second part is a joint work with O.K. Pashaev).
延伸閱讀
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