Research

Research Interest 

My research interests are analysis and differential equations in general. In particular, I study partial differential equations (PDEs) using both theoretical analysis and numerical simulations.  

My research is supported in part by the National Science Foundation  and the Simons Foundation.

Information

arXiv: https://arxiv.org/a/chen_g_5.html

Google Scholar file

Genealogy: https://www.genealogy.math.ndsu.nodak.edu/id.php?id=218434

MathSciNet: https://mathscinet.ams.org/mathscinet/author?authorId=1003678

Publications 

1. (With Yang Lan and Xu Yuan) On the near soliton dynamics for the 2D cubic Zakharov-Kuznetsov equations. arxiv: arXiv:2407.00300  

2. (With Francisco Alegría,  Claudio Muñoz, Felipe Poblete, Benjamín Tardy )On uniqueness of KP soliton structures. arXiv: arXiv:2405.07125  .

3. (with Jason Murphy ) Stability estimates for the recovery of the nonlinearity from scattering data.  Pure Appl. Anal. 6 (2024), no. 1, 305–317. arXiv: arXiv:2305.06170 

4. (with Jason Murphy ) Recovery of the nonlinearity from the modified scattering map.   Int. Math. Res. Not. IMRN(2024), no. 8, 6632–6655.. arXiv: arXiv:2304.01455  

5. (with Jacek Jendrej) Asymptotic stability and classification of multi-solitons for Klein-Gordon equations. Comm. Math. Phys. 405 (2024), no. 1, Paper No. 7, 47 pp arXiv:arXiv:2301.10279. 

6. (with Jacek Jendrej) Strichartz estimates for Klein-Gordon equations with moving potentials.  arXiv: arXiv:2210.03462  (submitted)

7.  (With Fabio Pusateri) On the 1d cubic NLS with a non-generic potential. Comm. Math. Phys. 405 (2024), no. 2, Paper No. 35, 59 pp.  arXiv: arXiv:2205.01487  

8. (with Jacek Jendrej) Kink networks for scalar fields in dimension 1 + 1. Nonlinear Anal. 215 (2022), Paper No. 112643. Special Section on Harmonic analysis, dispersive and wave equations; Edited by Yvan Martel, Claudio Muñoz, Gustavo Ponce.  arXiv: arXiv:2109.14342  

9. ( with Marius Beceanu) Strichartz estimates for the Klein-Gordon equation in R^{3+1}.  Pure Appl. Anal. 4 (2022), no. 4, 767–809..  arXiv: arXiv:2108.06390 

10.  Long-time dynamics of small solutions to 1d cubic nonlinear Schrödinger equations with a trapping potential. arXiv: arXiv:2106.10106. (submitted)

11. (with Qingtang Su) Nonlinear modulational instabililty of the Stokes waves in 2d full water waves. Comm. Math. Phys. 402 (2023), no. 2, 1345–1452. arXiv: arXiv:2012.15071 . 

12.  (with Jiaqi Liu  and Bingying Lu) Long-time asymptotics and stability for the sine-Gordon equation . arXiv: 2009.04260 (Submitted)

13. (with José M. Palacios)    Orbital stability and instability of periodic wave solutions for φ4n-models. Nonlinearity 36 (2023), no. 5, 2249–2285.  arXiv: 2008.04812. 

14.  (With Fabio Pusateri)  The 1d nonlinear Schrödinger equation with  a weighted-L^1 potential.  Anal. PDE 15 (2022), no. 4, 937–982  arXiv:1912.10949 

15.  (with Jiaqi Liu) Soliton resolution for the modified KdV Equation. Ann. Inst. H. Poincaré Anal. Non Linéaire. 38 (2021), no. 6, 2005–2071.  arXiv: 1907.07115 

16. (with Jiaqi Liu) Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces. Forum Math. Sigma 10 (2022), Paper No. e66, 52 pp.  arXiv:1903.03855  

17. (with Jacek Jendrej)  Lyapunov-type characterisation of exponential dichotomies with applications to the heat and Klein-Gordon equations. Trans. Amer. Math. Soc. 372 (2019) no. 10, pp. 7461–7496 . arXiv: 1812.07322. 

18.  Multisolitons for the defocusing energy critical wave equation with potentials. Comm. Math. Phys. 364 (2018), no. 1, 45–82.  arXiv:1705.03120

19.   Wave equations with moving potentials. Comm. Math. Phys. 375 (2020), no. 2, 1503–1560. arXiv:1610.09586. 

20.   Strichartz estimates for wave equations with charge transfer Hamiltonians, Mem. Amer. Math. Soc. 273 (2021), no. 1339, v + 84 pp. arXiv:1610.05226. 

21.  Strichartz estimates for charge transfer models. Discrete Contin. Dyn. Syst. 37 (2017), no. 3, 1201-1226. arXiv:1507.07644

22.  Non-divergence parabolic equations of second order with critical drift in Morrey spaces, arXiv:1602.00819.

23.  Non-divergence parabolic equations of second order with critical drift in Lebesgue spaces. J. Differential Equations 262 (2017), no. 3, 2414–2448. arXiv:1511.01215

24.   (with Mikhail Safonov) On second order elliptic and parabolic equations of mixed type. J. Functional Analysis 272 (2017), vol. 8, 3216–3237. arXiv:1401.0351

25.   (with Peter J. Olver) Numerical Simulation of Nonlinear Dispersive Quantization, Discrete Cont. Dyn. Syst. A  34 (2013), 991-1008. Link. PDF 

26.   (with Peter J. Olver) Dispersion of Discontinuous Periodic Waves, Proceedings of the Royal Society London A. 20120407. Link. PDF 

27. (with Brandon Cloutier, Benson K. Muite, etc.) Parallel spectral numerical methods and partial differential equations. (Shodor Education Foundation, (2012)) . Link.  PDF 

Permanent preprint 

1.   Long-time dynamics of small solutions to the Manakov system with initial data in the weighted $L^{2}$ space. PDF  

Conference proceedings and reports

1. The 1d cubic NLS with a non-generic potential. Extended abstract of Oberwolfach workshop 2226.  link

Movies for dispersive quantization

1.  Movies of Linear Dispersion on a Periodic Domain. link

2.  Movies of Nonlinear Dispersion on a Periodic Domain. link

Thesis and Expository Notes

• Vibrations of suspended chains.

My undergrad honors thesis from the University of Minnesota.

• Holomorphic functional calculus and some application.

Analysis III final project. They were written during my first year at the University of Chicago.

• Dispersive estimates, Strichartz estimates and smoothing effects.

They were written during my second year at the University of Chicago as part of my topics examination. 

• Dispersive equations with multiple potentials. ProQuest

 My PhD thesis from the University of Chicago.