We study the work of professor M Ohta ”Stability of solitary waves for the Zakharov equations in one space dimension” and the work of professor M Maeda ”Stability of ground states of NLS with fourth order dispersion” then elaborate details in this article In both papers we discuss the solitary wave solutions of the equations also known as standing wave solution and the stability With the lowest energy the solution is stable We first discuss the Zakharov equation and use the similarities between the Zakharov equation and the Schr?dinger equation to complete the proof using variational approach In professor M Maeda’s paper we discuss the Schr?dinger equation with a fourth-order derivative term With small parameter in fourth-order term the minimum energy solution of the two dimensional Schr?dinger equation is stable In addition to reading these two papers we also added some details that the authors omitted as well as some errors in printing
Stability of Solitary Waves for the Zakharov Equations and the Fourth Order Nonlinear Schr"{o}dinger Equation
雅琳, 黃. (Author). 2018 7月 18
學生論文: Master's Thesis