We study the dynamics of the collision of two solitary waves for the 2 and 3-dimensional
Zakharov–Kuznetsov equation, a high-dimensional non-integrable version of the Korteweg …

We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the
Zakharov–Kuznetsov equation in dimensions two and three. We also derive a qualitative …

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 study stability properties of solitary wave solutions for the fractional generalized
Korteweg-de Vries equation $$\partial_t u-\partial_ {x_1} D^{\alpha} u+\tfrac {1}{m}\partial …

We derive the Whitham modulation equations for the Zakharov–Kuznetsov equation via a
multiple scales expansion and averaging two conservation laws over one oscillation period …

This work mainly focuses on spatial decay properties of solutions to the Zakharov–
Kuznetsov equation. For the two-and three-dimensional cases, it was established that if the …

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 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 …

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 …