My current research interests lie in the areas of water waves, dispersive PDEs and nonlinear waves on graphs.

Below is the list of publications split by topics:

Water Waves

• Guyenne P., Kairzhan A. and Sulem C. A Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticity. J. Fluid Mech. 949 (2022). Link

• Guyenne P., Kairzhan A. and Sulem C. Hamiltonian Dysthe Equation for Three-Dimensional Deep-Water Gravity Waves, SIAM: Mult. Model. Simul. 20, no. 1 (2022) pp. 349-378. Link

• Guyenne P., Kairzhan A. and Sulem C. Normal form transformations for modulated deep-water gravity waves, Rev. de la Un. Mat. Arg. - Spec. Iss: MCA (2022) accepted. Link

• Guyenne P., Kairzhan A., Sulem C. and Xu B. Spatial Form of a Hamiltonian Dysthe Equation for Deep-Water Gravity Waves. Fluids 6, no. 3 (2021) 103. Link

Stability in Dispersive PDEs

• Kairzhan A. and Pusateri F. Asymptotic stability near the soliton for quartic Klein-Gordon in 1D. Preprint arXiv:2206.15008 (2022) submitted.

Nonlinear Waves on Graphs

• Kairzhan A., Noja D. and Pelinovsky D. Standing waves on quantum graphs. J. Phys. A: Math. Theor. 55 (2022) 243001. Link

• Kairzhan A. and Pelinovsky D. Multi-pulse edge-localized states on quantum graphs. Anal. and Math. Phys. 11 (2021) 171. Link

• Kairzhan A., Marangell R., Pelinovsky D. and Xiao K. Standing waves on a flower graph. J. Diff. Eq. 271 (2021) pp. 719-763. Link

• Kairzhan A., Pelinovsky D. and Goodman R. Drift of spectrally stable shifted states on star graphs. SIAM J. Appl. Dyn. Syst. 18 (2019) pp. 1723-1755. Link

• Kairzhan A. Orbital instability of standing waves for NLS equation on star graphs. Proc. AMS 147 (2019) pp. 2911-2924. Link

• Kairzhan A. and Pelinovsky D. Spectral stability of shifted states on star graphs. J. Phys. A: Math. Theor. 51 (2018) 095203. Link

• Kairzhan A. and Pelinovsky D. Nonlinear instability of half-solitons on star graphs. J. Diff. Eq. 264, no.12 (2018) pp. 7357-7383. Link