2018年海洋信息论坛第23期
报告题目： On the two different approaches to the derivation of parabolic equations
报告人：Dr. Pavel S. Petrov
时间：
地点：水声楼15楼学术报告厅
报告人简介：
Pavel S. Petrov于2009年获得伊尔库茨克州立大学(Irkutsk State University)数学专业的硕士学位，于2012年获得太平洋研究所(Il’ichev Pacific Oceanological Institute)理论物理专业的正博士学位。自2012年至今，Pavel S. Petrov博士在太平洋研究所担任研究员职位，同时在远东联邦大学(Far Eastern Federal University)兼任副教授职位。期间他两次以洪堡学者奖学金获得者的身份前往德国高校进行访问和进修，并在以色列海法大学Boris Katsnelson教授处做过短期博后。由于在三维声传播模型方面发表了一系列高质量文章，太平洋研究所于2017年授予Pavel S. Petrov博士以“声学与海洋研究领域年轻科学家伊利切夫奖”。
Pavel S. Petrov博士的研究专长包括声传播、吸收与散射、计算海洋声学、波动过程数学建模、渐进方法等。Pavel S. Petrov博士尤其在三维海洋声传播及其应用方面颇有造诣，他编写的多项三维声场计算代码已上传至水声领域著名开源网站Ocean Acoustics Library，可供免费使用。
报告简介：
The historical overview of different techniques for the derivation of paraxial propagation equations (or parabolic equations) is given, and the original motivation from radiowaves theory is outlined. The concept of the iterative parabolic approximation based on the multiscale technique is discussed. This approach is compared with the traditional ways of the wide-angle parabolic equation derivation. Advantages and disadvantages of both derivation methods are discussed. The interface and boundary conditions for both cases are considered in the context of acoustical applications. Two classical problems of underwater acoustics are considered. A convergence theorem for the iterative parabolic equation is proven. It is shown that the multiscale derivation technique leading to iterative parabolic equations can be easily adapted to handle the case of nonlinear Helmholtz equation. The nonlinear iterative parabolic approximations for the wave propagation in (optical) Kerr media are presented. An example demonstrating the capability of iterative parabolic equations to take nonparaxial propagation effects in nonlinear media into account is considered.