相关论文: Spectral property for the 2D Zakharov-Kuznetsov eq…
We investigate the instability index of the spectral problem $$ -c^2y'' + b^2y + V(x)y = -\mathrm{i} z y' $$ on the line $\mathbb{R}$, where $V\in L^1_{\rm loc}(\mathbb{R})$ is real valued and $b,c>0$ are constants. This problem arises in…
The heavy ion acoustic solitary waves (HIASWs) in a magnetized, collisionless, three component space plasma system in the presence of dynamical heavy particles and bi-kappa distributed two distinct temperature of electrons has been carried…
The KdV-Sawada-Kotera equation has single-, two- and three-soliton solutions. However, it is not known yet whether it has N-soliton solutions for any N. Viewing it as a perturbed KdV equation, the asymptotic expansion of the solution is…
An initial-boundary value problem for the critical generalized 2D Zakharov-Kuznetsov equation posed on a half-strip is considered. Existence, uniqueness and the exponential decay rate of global regular solutions for small initial data are…
Motivated by the recent Magnetospheric Multiscale (MMS) observations of oblique electron acoustic waves, we addressed the generation mechanism of the observed waves by utilizing the reductive perturbation technique. The nonlinear…
We study the Klein-Gordon-Zakharov system in two spatial dimensions, an important model in plasma physics. For small, smooth, and spatially localized initial data, we establish the global existence of solutions and characterize their sharp…
We study the spectral properties of the linearized Euler operator obtained by linearizing the equations of incompressible two dimensional fluid at a steady state with the vorticity that contains only two nonzero complex conjugate Fourier…
We present a general counting result for the unstable eigenvalues of linear operators of the form $JL$ in which $J$ and $L$ are skew- and self-adjoint operators, respectively. Assuming that there exists a self-adjoint operator $K$ such that…
We study a quasilinear Schr\"odinger equation with nonzero conditions at infinity. In previous works, we obtained a continuous branch of traveling waves, given by dark solitons indexed by their speed. Neglecting the quasilinear term, one…
The work presented here emanates from questions arising from experimental observations of the propagation of surface water waves. The experiments in question featured a periodically moving wavemaker located at one end of a flume that…
The singular real second order 1D Schrodinger operators are considered here with such potentials that all local solutions near singularities to the eigenvalue problem are meromorphic for all values of the spectral parameter. All…
The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects. Although this equation has only one conservation law, exact…
We consider the extended Korteweg-de Vries (eKdV) equation as a model for long moderately nonlinear surface water waves. In the slow time formulation this equation generates fast propagating resonant radiation due to the non-convexity of…
We consider families of solitary waves in the Korteweg--de Vries (KdV) equation coupled with the linear Schr\"{o}dinger (LS) equation. This model has been used to describe interactions between long and short waves. To characterize families…
Three (2+1)-dimensional equations, they are KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave…
The Kadomtsev--Petviashvili I (KPI) is considered as a useful laboratory for experimenting new theoretical tools able to handle the specific features of integrable models in $2+1$ dimensions. The linearized version of the KPI equation is…
The $b$-family-Kadomtsev-Petviashvili equation ($b$-KP) is a two dimensional generalization of the $b$-family equation. In this paper, we study the spectral stability of the one-dimensional small-amplitude periodic traveling waves with…
This work is a continuation of our previos paper \cite{Zel1}, where for the the Schr\"odinger operator $H=-\Delta+ V(\e)\cdot$ $(V(\e)\ge 0)$, acting in the space $L_2(\R^d)\,(d\ge 3)$, some constructive sufficient conditions for…
Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in classes of regular solutions in the cases of…
In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up…