209 citations · 1.4k across the 114 of their papers we have counts for
17 papers · 1 filter
Variable-coefficient symbolic computation approach for finding multiple rogue wave solutions of nonlinear system with variable coefficients
Jian-Guo Liu, Wen-Hui Zhu, Yan He
In this paper, a variable-coefficient symbolic computation approach is proposed to solve the multiple rogue wave solutions of nonlinear equation with variable coefficients. As an a…
Field model for complex ionic fluids: analytical properties and numerical investigation
Jian-Guo Liu, Jinhuan Wang, Yu Zhao +1
In this paper, we consider the field model for complex ionic fluids with an energy variational structure, and analyze the well-posedness to this model with regularized kernels. Fur…
Multiple rogue wave solutions for (2+1)-dimensional Boussinesq equation
Jian-Guo Liu, Wen-Hui Zhu
In this paper, a modified symbolic computation approach is proposed. The multiple rogue wave solutions of a generalized (2+1)-dimensional Boussinesq equation are obtained by using…
Interaction phenomena between lump and solitary wave of a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation in liquid with gas bubbles
Jian-Guo Liu, Wen-Hui Zhu, Yan He +1
In this paper, a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota's bilinear form and symboli…
A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration
Jingwei Hu, Jian-Guo Liu, Yantong Xie +1
In this work, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at…
Stripe solitons and lump solutions to a generalized (3 + 1)-dimensional B-type Kadomtsev-Petviashvili equation with variable coefficients in fluid dynamics
Wen-Hui Zhu, Jian-Guo Liu
Under investigation is a generalized (3 + 1)-dimensional B-type Kadomtsev-Petviashvili equation with variable coefficients in fluid dynamics. Based on the Hirota's bilinear form an…
Multiple rogue wave solutions for the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation
Jian-Guo Liu, Huan Zhao
Based on the symbolic computation approach, multiple rogue wave solutions of the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation are studied. As an examp…
Multi-wave, breather wave and lump solutions of the Boiti-Leon-Manna-Pempinelli equation with variable coefficients
Jian-Guo Liu, Wang-Ping Xiong
In this paper, a variable-coefficient Boiti-Leon-Manna-Pempinelli equation is to be investigated. We obtain abundant multi-wave, breather wave and lump solutions by using the three…
Towards understanding the boundary propagation speeds in tumor growth models
Jian-Guo Liu, Min Tang, Li Wang +1
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific…
Mathematical validation of the Peierls--Nabarro model for edge dislocations
Yuan Gao, Jian-Guo Liu, Tao Luo +1
In this paper, we perform mathematical validation of the Peierls--Nabarro (PN) models, which are multiscale models of dislocations that incorporate the detailed dislocation core st…
Long time behavior of dynamic solution to Peierls--Nabarro dislocation model
Yuan Gao, Jian-Guo Liu
In this paper we study the relaxation process of Peierls-Nabarro dislocation model, which is a gradient flow with singular nonlocal energy and double well potential describing how…
Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects
Yuan Gao, Jian-Guo Liu, Jianfeng Lu +1
We study a th order PDE with a nd order correction that is a modification of one suggested by Peter Smereka using the tools of Krug et al (Z. Phys. B., 1994). First, we provi…
Self-similar spreading in a merging-splitting model of animal group size
Jian-Guo Liu, Barbara Niethammer, Robert L. Pego
In a recent study of certain merging-splitting models of animal-group size (Degond et al., J. Nonl. Sci. 27 (2017) 379), it was shown that an initial size distribution with infinit…
A stochastic version of Stein Variational Gradient Descent for efficient sampling
Lei Li, Yingzhou Li, Jian-Guo Liu +2
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful…
Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
Yuanyuan Feng, Tingran Gao, Lei Li +2
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the back…
A Markov jump process modelling animal group size statistics
Pierre Degond, Maximilian Engel, Jian-Guo Liu +1
We translate a coagulation-framentation model, describing the dynamics of animal group size distributions, into a model for the population distribution and associate the \blue{nonl…
A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows
Lei Li, Jian-Guo Liu
We consider a discretization of Caputo derivatives resulted from deconvolving a scheme for the corresponding Volterra integral. Properties of this discretization, including signs o…