-
Previous Article
Generalizations of logarithmic Sobolev inequalities
- DCDS-S Home
- This Issue
-
Next Article
Dynamics of ratio-dependent Predator-Prey models with nonconstant harvesting
Modeling thermal effects on nonlinear wave motion in biopolymers by a stochastic discrete nonlinear Schrödinger equation with phase damping
| 1. | Department of Mathematics, College of Charleston, Charleston, SC, 29424, United States |
New numerical methods are introduced to handle the unusual combination of a conservative equation, stochastic, and fully nonlinear terms. Some analysis is given of accuracy needs, and the special issues of time step adjustment in stochastic realizations. Numerical studies are presented of the effects of thermalization on solitons, including damping induced self-trapping of wave energy, a discrete counterpart of single-point blowup.
| [1] |
Henryk Leszczyński, Monika Wrzosek. Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion. Mathematical Biosciences & Engineering, 2017, 14 (1) : 237-248. doi: 10.3934/mbe.2017015 |
| [2] |
Kexue Li. Effects of the noise level on nonlinear stochastic fractional heat equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5437-5460. doi: 10.3934/dcdsb.2019065 |
| [3] |
Cynthia Ferreira, Guillaume James, Michel Peyrard. Nonlinear lattice models for biopolymers: Dynamical coupling to a ionic cloud and application to actin filaments. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1147-1166. doi: 10.3934/dcdss.2011.4.1147 |
| [4] |
Wei Wang, Yan Lv. Limit behavior of nonlinear stochastic wave equations with singular perturbation. Discrete and Continuous Dynamical Systems - B, 2010, 13 (1) : 175-193. doi: 10.3934/dcdsb.2010.13.175 |
| [5] |
Letizia Stefanelli, Ugo Locatelli. Kolmogorov's normal form for equations of motion with dissipative effects. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2561-2593. doi: 10.3934/dcdsb.2012.17.2561 |
| [6] |
Jingyu Wang, Yejuan Wang, Lin Yang, Tomás Caraballo. Random attractors for stochastic delay wave equations on $ \mathbb{R}^n $ with linear memory and nonlinear damping. Discrete and Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021141 |
| [7] |
Yong Ren, Wensheng Yin, Dongjin Zhu. Exponential stability of SDEs driven by $G$-Brownian motion with delayed impulsive effects: average impulsive interval approach. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3347-3360. doi: 10.3934/dcdsb.2018248 |
| [8] |
Guolian Wang, Boling Guo. Stochastic Korteweg-de Vries equation driven by fractional Brownian motion. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5255-5272. doi: 10.3934/dcds.2015.35.5255 |
| [9] |
J. C. Dallon, Lynnae C. Despain, Emily J. Evans, Christopher P. Grant. A continuous-time stochastic model of cell motion in the presence of a chemoattractant. Discrete and Continuous Dynamical Systems - B, 2020, 25 (12) : 4839-4852. doi: 10.3934/dcdsb.2020129 |
| [10] |
Defei Zhang, Ping He. Functional solution about stochastic differential equation driven by $G$-Brownian motion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 281-293. doi: 10.3934/dcdsb.2015.20.281 |
| [11] |
Yong Xu, Rong Guo, Di Liu, Huiqing Zhang, Jinqiao Duan. Stochastic averaging principle for dynamical systems with fractional Brownian motion. Discrete and Continuous Dynamical Systems - B, 2014, 19 (4) : 1197-1212. doi: 10.3934/dcdsb.2014.19.1197 |
| [12] |
Yong Xu, Bin Pei, Rong Guo. Stochastic averaging for slow-fast dynamical systems with fractional Brownian motion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2257-2267. doi: 10.3934/dcdsb.2015.20.2257 |
| [13] |
Tai-Chia Lin. Vortices for the nonlinear wave equation. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 391-398. doi: 10.3934/dcds.1999.5.391 |
| [14] |
Vivek Tewary. Combined effects of homogenization and singular perturbations: A bloch wave approach. Networks and Heterogeneous Media, 2021, 16 (3) : 427-458. doi: 10.3934/nhm.2021012 |
| [15] |
Q-Heung Choi, Tacksun Jung. A nonlinear wave equation with jumping nonlinearity. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 797-802. doi: 10.3934/dcds.2000.6.797 |
| [16] |
Út V. Lê. Regularity of the solution of a nonlinear wave equation. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1099-1115. doi: 10.3934/cpaa.2010.9.1099 |
| [17] |
Jorge A. Esquivel-Avila. Qualitative analysis of a nonlinear wave equation. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 787-804. doi: 10.3934/dcds.2004.10.787 |
| [18] |
Nakao Hayashi, Pavel I. Naumkin, Patrick-Nicolas Pipolo. Smoothing effects for some derivative nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 685-695. doi: 10.3934/dcds.1999.5.685 |
| [19] |
Antony R. Humphries, Bernd Krauskopf, Stefan Ruschel, Jan Sieber. Nonlinear effects of instantaneous and delayed state dependence in a delayed feedback loop. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022042 |
| [20] |
Feng Rao, Carlos Castillo-Chavez, Yun Kang. Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1401-1423. doi: 10.3934/mbe.2018064 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]