44 citations · 176 across the 20 of their papers we have counts for
21 papers
Structurally stable singularities and Lipschitz stable optimal transport metrics for the compressible Euler equations
Geng Chen, Yanbo Hu, Yannan Shen
It is well known that solutions to the compressible Euler equations can develop singularities in finite time. In this paper, we carry out a detailed analysis on behaviors of soluti…
The contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock
Geng Chen, Harish Ravichandar, Yannan Shen
In this paper, we show the contraction property of the planar oscillatory or monotone dispersive shock profiles of the dissipative Kadomtsev-Petviashvili (KP) equation modell…
-contraction of Shock Waves for KdV-Burgers Equation
Geng Chen, Namhyun Eun, Moon-Jin Kang +1
The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave sol…
Uniform Stability of Oscillatory Shocks for KdV-Burgers Equation
Geng Chen, Namhyun Eun, Moon-Jin Kang +1
We study viscous-dispersive shock waves with infinite oscillations of the Korteweg-de Vries-Burgers (KdVB) equation. First, we establish detail structures of the shock waves, inclu…
Singularity formation for the supersonic inward wave of compressible Euler equations with radial symmetry
Geng Chen, Faris A. El-Katri, Yanbo Hu +1
In this paper, we consider the singularity formation of smooth solutions for the compressible radially symmetric Euler equations. By applying the characteristic method and the inva…
Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry
Geng Chen, Faris A. El-Katri, Yanbo Hu +1
In this paper, we define the rarefaction and compression characters for the supersonic expanding wave of the compressible Euler equations with radial symmetry. Under this new defin…
Lipschitz optimal transport metric for a wave system modeling nematic liquid crystals
Hong Cai, Geng Chen, Yannan Shen
In this paper, we study the Lipschitz continuous dependence of conservative Hölder continuous weak solutions to a variational wave system derived from a model for nematic liquid cr…
Spatiotemporal dynamics in a twisted, circular waveguide array
Ross Parker, Yannan Shen, Alejandro Aceves +1
We consider the existence and spectral stability of nonlinear discrete localized solutions representing light pulses propagating in a twisted multi-core optical fiber. By consideri…
Existence and regularity for global solutions including breaking waves from Camassa-Holm and Novikov equations to -family equations
Geng Chen, Yannan Shen, Shihui Zhu
In this paper, we prove the global existence of Hölder continuous solutions for the Cauchy problem of a family of partial differential equations, named as -family equations, whe…
Spectral computation of low probability tails for the homogeneous Boltzmann equation
John Zweck, Yanping Chen, Matthew J. Goeckner +1
We apply the spectral-Lagrangian method of Gamba and Tharkabhushanam for solving the homogeneous Boltzmann equation to compute the low probability tails of the velocity distributio…
Uniqueness of conservative solutions to a one-dimensional general quasilinear wave equation through variational principle
Hong Cai, Geng Chen, Yi Du +1
In this paper, we prove the uniqueness of energy conservative Holder continuous weak solution to a general quasilinear wave equation by the analysis of characteristics. This result…
From Solitons to Rogue Waves in Nonlinear Left-Handed Metamaterials
Yannan Shen, P. G. Kevrekidis, G. P. Veldes +4
In the present work, we explore soliton and rogue-like wave solutions in the transmission line analogue of a nonlinear left-handed metamaterial. The nonlinearity is expressed throu…
Lipschitz metric for the Novikov equation
Hong Cai, Geng Chen, Robin MIng Chen +1
We consider the Lipschitz continuous dependence of solutions for the Novikov equation with respect to the initial data. In particular, we construct a Finsler type optimal transport…
Light dynamics in nonlinear trimers and twisted multicore fibers
Claudia Castro-Castro, Yannan Shen, Gowri Srinivasan +2
Novel photonic structures such as multi-core fibers and graphene based arrays present unique opportunities to manipulate and control the propagation of light. Here we discuss nonli…
Existence and regularity of solutions in nonlinear wave equations
Geng Chen, Yannan Shen
In this paper, we study the global existence and regularity of Hölder continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.
Characterizing Traveling Wave Collisions in Granular Chains Starting from Integrable Limits: the case of the KdV and the Toda Lattice
Y. Shen, P. G. Kevrekidis, S. Sen +1
Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To tha…
Traveling waves of the regularized short pulse equation
Y. Shen, T. P. Horikis, P. G. Kevrekidis +1
In the present work, we revisit the so-called regularized short pulse equation (RSPE) and, in particular, explore the traveling wave solutions of this model. We theoretically analy…
Ultrashort pulses and short-pulse equations in dimensions
Y. Shen, N. Whitaker, P. G. Kevrekidis +2
In this paper, we derive and study two versions of the short pulse equation (SPE) in dimensions. Using Maxwell's equations as a starting point, and suitable Kramers-Kronig…
Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: an example of an anti-damped Josephson junction
Y. Shen, P. G. Kevrekidis, N. Whitaker +2
We study matter-wave dark solitons in atomic Bose-Einstein condensates at finite temperatures, under the effect of linear and periodic potentials. Our model, namely a dissipative G…
Spatial solitons under competing linear and nonlinear diffractions
Y. Shen, P. G. Kevrekidis, N. Whitaker +1
We introduce a general model which augments the one-dimensional nonlinear Schrödinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new t…
Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials
N. L. Tsitsas, T. P. Horikis, Y. Shen +3
We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. In the frequency "band gaps" (where line…