35 citations · 88 across the 9 of their papers we have counts for
14 papers
Global dynamics for the 1d quartic Klein-Gordon equation with an internal mode
Gong Chen, Gael Y. Diebou, Adilbek Kairzhan +1
We study a one dimensional nonlinear Klein-Gordon equation with a potential, a localized quadratic nonlinearity, and a non-localized quartic nonlinearity. We assume that the linear…
Traveling Waves for Nonlocal Derivative Nonlinear Schrödinger Equations: A Variational Characterization
Amin Esfahani, Adilbek Kairzhan, Mukhtar Karazym
We establish several existence results for traveling-wave solutions of the nonlocal derivative nonlinear Schrödinger equation with general coefficients by variational methods. We s…
A Hamiltonian Dysthe equation for hydroelastic waves in a compressed ice sheet
Philippe Guyenne, Adilbek Kairzhan, Catherine Sulem
Nonlinear hydroelastic waves along a compressed ice sheet lying on top of a two-dimensional fluid of infinite depth are investigated. Based on a Hamiltonian formulation of this pro…
Interaction between long internal waves and free surface waves in deep water
Adilbek Kairzhan, Christopher Kennedy, Catherine Sulem
We consider a density-stratified fluid composed of two immiscible layers separated by a sharp interface. We study the regime of long internal waves interacting with modulated surfa…
Asymptotic stability near the soliton for quartic Klein-Gordon in 1D
Adilbek Kairzhan, Fabio Pusateri
We consider the nonlinear focusing Klein-Gordon equation in dimensions and the global space-time dynamics of solutions near the unstable soliton. Our main result is a proof…
A Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticity
Philippe Guyenne, Adilbek Kairzhan, Catherine Sulem
This paper is a study of the water wave problem in a two-dimensional domain of infinite depth in the presence of nonzero constant vorticity. A goal is to describe the effects of un…
Standing waves on quantum graphs
Adilbek Kairzhan, Diego Noja, Dmitry E. Pelinovsky
We review evolutionary models on quantum graphs expressed by linear and nonlinear partial differential equations. Existence and stability of the standing waves trapped on quantum g…
Hamiltonian Dysthe equation for 3D deep-water gravity waves
Philippe Guyenne, Adilbek Kairzhan, Catherine Sulem
This article concerns the water wave problem in a three-dimensional domain of infinite depth and examines the modulational regime for weakly nonlinear wavetrains. We use the method…
Multi-pulse edge-localized states on quantum graphs
Adilbek Kairzhan, Dmitry E. Pelinovsky
Edge-localized stationary states of the focusing nonlinear Schrodinger equation on a general quantum graph are considered in the limit of large mass. Compared to the previous works…
Standing waves on a flower graph
Adilbek Kairzhan, Robert Marangell, Dmitry E. Pelinovsky +1
A flower graph consists of a half line and symmetric loops connected at a single vertex with (it is called the tadpole graph if ). We consider positive single…
Drift of spectrally stable shifted states on star graphs
Adilbek Kairzhan, Dmitry E. Pelinovsky, Roy H. Goodman
When the coefficients of the cubic terms match the coefficients in the boundary conditions at a vertex of a star graph and satisfy a certain constraint, the nonlinear Schrödinger (…
Orbital instability of standing waves for NLS equation on Star Graphs
Adilbek Kairzhan
We consider a nonlinear Schrödinger (NLS) equation with any positive power nonlinearity on a star graph ( half-lines glued at the common vertex) with a interaction at th…
Spectral stability of shifted states on star graphs
Adilbek Kairzhan, Dmitry E. Pelinovsky
We consider the nonlinear Schrödinger (NLS) equation with the subcritical power nonlinearity on a star graph consisting of edges and a single vertex under generalized Kirchhoff…
Nonlinear Instability of Half-Solitons on Star Graphs
Adilbek Kairzhan, Dmitry E. Pelinovsky
We consider a half-soliton stationary state of the nonlinear Schrodinger equation with the power nonlinearity on a star graph consisting of N edges and a single vertex. For the sub…