几类重要 Wick 型分数阶随机非线性偏微分方程的行波解
偏微分方程分析
2020-02-18 v2 数值分析
数值分析
摘要
本文利用一种改进的计算方法，获得了 Wick 型随机非线性 Schr"{o}dinger 方程与 Wick 型随机分数阶正则长波-Burgers (RLW-Burgers) 方程的精确行波解。具体而言，采用 Hermite 变换将 Wick 型随机非线性偏微分方程转化为具有整数阶与分数阶的确定性非线性偏微分方程。进而，利用逆 Hermite 变换得到白噪声空间中所需的随机解集合。基于导出的解，在物理参数的若干特定取值下对所述方程进行了动力学分析。结果表明，所提出的改进计算技术可应用于求解各类 Wick 型随机分数阶偏微分方程。
引用
@article{arxiv.1911.08903,
title = {Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations},
author = {Hyunsoo Kim and Rathinasamy Sakthivel and Amar Debbouche and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1911.08903},
year = {2020}
}
备注
This is a preprint of a paper whose final and definite form is with 'Chaos, Solitons & Fractals', ISSN 0960-0779 [https://doi.org/10.1016/j.chaos.2019.109542]. Submitted 19-Sept-2019; Revised 14-Nov-2019; Accepted for publication 18-Nov-2019. This version includes minor corrections detected while reading galley proofs