Abstract We consider the Zakharov-Kutznesov (ZK) equation posed in R d, with d= 2 and 3.
Both equations are globally well-posed in L 2 (R d). In this article, we prove local energy …

In this article, we consider the Cauchy problem for the cubic (mass-critical) Zakharov-
Kuznetsov equations in dimension two: $$\partial_t u+\partial_ {x_1}(\Delta u+ u^ 3) …

We present a detailed numerical study of solutions to the (generalized) Zakharov–Kuznetsov
equation in two spatial dimensions with various power nonlinearities. In the L^ 2 L 2 …

We consider the generalized Benjamin-Ono (gBO) equation on the real line, u t+∂ x (− H u
x+ 1 mum)= 0, x∈ R, m= 2, 3, 4, 5, and perform numerical study of its solutions. We first …

We study here the Zakharov-Kuznetsov equation in dimension $2 $, $3 $ and $4 $ and the
modified Zakharov-Kuznetsov equation in dimension $2 $. Those equations admit solitons …

We consider the quadratic Zakharov-Kuznetsov equation $$\partial_t u+\partial_x\Delta
u+\partial_x u^ 2= 0$$ on $\Bbb {R}^ 3$. A solitary wave solution is given by $ Q (xt, y, z) …

We present a detailed numerical study of solutions to the Zakharov–Kuznetsov equation in
three spatial dimensions. The equation is a three-dimensional generalization of the …

In this paper we prove rigidity for blowup solutions to the focusing, mass-critical nonlinear
Schrödinger equation in dimensions 2≤ d≤ 15 with mass equal to the mass of the soliton …

For the 2D cubic (mass-critical) Zakharov-Kuznetsov equation,\begin {equation*}\partial_t\
phi+\partial_ {x_1}(\Delta\phi+\phi^ 3)= 0,\quad (t, x)\in [0,\infty)\times\mathbb {R}^{2},\end …

We present a detailed numerical study of the stability under periodic perturbations of line
solitons of two-dimensional, generalized Zakharov–Kuznetsov equations with various power …