
Previous Article
Generalizations of logarithmic Sobolev inequalities
 DCDSS Home
 This Issue

Next Article
Dynamics of ratiodependent PredatorPrey 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 selftrapping of wave energy, a discrete counterpart of singlepoint blowup.
[1] 
Henryk Leszczyński, Monika Wrzosek. Newton's method for nonlinear stochastic wave equations driven by onedimensional Brownian motion. Mathematical Biosciences & Engineering, 2017, 14 (1) : 237248. doi: 10.3934/mbe.2017015 
[2] 
Kexue Li. Effects of the noise level on nonlinear stochastic fractional heat equations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (10) : 54375460. 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 & Continuous Dynamical Systems  S, 2011, 4 (5) : 11471166. doi: 10.3934/dcdss.2011.4.1147 
[4] 
Wei Wang, Yan Lv. Limit behavior of nonlinear stochastic wave equations with singular perturbation. Discrete & Continuous Dynamical Systems  B, 2010, 13 (1) : 175193. doi: 10.3934/dcdsb.2010.13.175 
[5] 
Letizia Stefanelli, Ugo Locatelli. Kolmogorov's normal form for equations of motion with dissipative effects. Discrete & Continuous Dynamical Systems  B, 2012, 17 (7) : 25612593. doi: 10.3934/dcdsb.2012.17.2561 
[6] 
Yong Ren, Wensheng Yin, Dongjin Zhu. Exponential stability of SDEs driven by $G$Brownian motion with delayed impulsive effects: average impulsive interval approach. Discrete & Continuous Dynamical Systems  B, 2018, 23 (8) : 33473360. doi: 10.3934/dcdsb.2018248 
[7] 
Guolian Wang, Boling Guo. Stochastic Kortewegde Vries equation driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems, 2015, 35 (11) : 52555272. doi: 10.3934/dcds.2015.35.5255 
[8] 
J. C. Dallon, Lynnae C. Despain, Emily J. Evans, Christopher P. Grant. A continuoustime stochastic model of cell motion in the presence of a chemoattractant. Discrete & Continuous Dynamical Systems  B, 2020, 25 (12) : 48394852. doi: 10.3934/dcdsb.2020129 
[9] 
Defei Zhang, Ping He. Functional solution about stochastic differential equation driven by $G$Brownian motion. Discrete & Continuous Dynamical Systems  B, 2015, 20 (1) : 281293. doi: 10.3934/dcdsb.2015.20.281 
[10] 
Yong Xu, Rong Guo, Di Liu, Huiqing Zhang, Jinqiao Duan. Stochastic averaging principle for dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2014, 19 (4) : 11971212. doi: 10.3934/dcdsb.2014.19.1197 
[11] 
Yong Xu, Bin Pei, Rong Guo. Stochastic averaging for slowfast dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2015, 20 (7) : 22572267. doi: 10.3934/dcdsb.2015.20.2257 
[12] 
Vivek Tewary. Combined effects of homogenization and singular perturbations: A bloch wave approach. Networks & Heterogeneous Media, 2021 doi: 10.3934/nhm.2021012 
[13] 
TaiChia Lin. Vortices for the nonlinear wave equation. Discrete & Continuous Dynamical Systems, 1999, 5 (2) : 391398. doi: 10.3934/dcds.1999.5.391 
[14] 
Feng Rao, Carlos CastilloChavez, Yun Kang. Dynamics of a stochastic delayed Harrisontype predation model: Effects of delay and stochastic components. Mathematical Biosciences & Engineering, 2018, 15 (6) : 14011423. doi: 10.3934/mbe.2018064 
[15] 
Nakao Hayashi, Pavel I. Naumkin, PatrickNicolas Pipolo. Smoothing effects for some derivative nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems, 1999, 5 (3) : 685695. doi: 10.3934/dcds.1999.5.685 
[16] 
QHeung Choi, Tacksun Jung. A nonlinear wave equation with jumping nonlinearity. Discrete & Continuous Dynamical Systems, 2000, 6 (4) : 797802. doi: 10.3934/dcds.2000.6.797 
[17] 
Út V. Lê. Regularity of the solution of a nonlinear wave equation. Communications on Pure & Applied Analysis, 2010, 9 (4) : 10991115. doi: 10.3934/cpaa.2010.9.1099 
[18] 
Jorge A. EsquivelAvila. Qualitative analysis of a nonlinear wave equation. Discrete & Continuous Dynamical Systems, 2004, 10 (3) : 787804. doi: 10.3934/dcds.2004.10.787 
[19] 
María J. Garrido–Atienza, Kening Lu, Björn Schmalfuss. Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 473493. doi: 10.3934/dcdsb.2010.14.473 
[20] 
Jin Li, Jianhua Huang. Dynamics of a 2D Stochastic nonNewtonian fluid driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2012, 17 (7) : 24832508. doi: 10.3934/dcdsb.2012.17.2483 
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]