Zobrazeno 1 - 10
of 159 097
pro vyhledávání: '"Zakharov, A"'
We study the convergence of a Zakharov system driven by a time white noise, colored in space, to a multiplicative stochastic nonlinear Schr{\"o}dinger equation, as the ion-sound speed tends to infinity. In the absence of noise, the conservation of en
Externí odkaz:
http://arxiv.org/abs/2409.14777
Autor:
Shan, Minjie
In this paper, we discuss pointwise decay estimate for the solution to the mass-critical generalized Korteweg-de Vries (gKdV) equation with initial data $u_0\in H^{1/2}(\mathbb{R})$. It is showed that nonlinear solution enjoys the same decay rate as
Externí odkaz:
http://arxiv.org/abs/2409.05550
This work is devoted to the stochastic Zakharov system in dimension four, which is the energy-critical dimension. First, we prove local well-posedness in the energy space $H^1\times L^2$ up to the maximal existence time and a blow-up alternative. Sec
Externí odkaz:
http://arxiv.org/abs/2410.05034
The influence of fractional order parameter $(\alpha)$ in nonlinear waves is examined in the fractional Zakharov-Kuznetsov (FZK) equation with the Hirota bilinear approach. Symbolic computation is used for all mathematical calculations. A significant
Externí odkaz:
http://arxiv.org/abs/2409.18993
Autor:
Baldasso, Mikaela, Panthee, Mahendra
We consider the initial value problem (IVP) for the 2D generalized Zakharov-Kuznetsov (ZK) equation \begin{equation} \begin{cases} \partial_{t}u+\partial_{x}\Delta u+\mu \partial_{x}u^{k+1}=0, \,\;\; (x, y) \in \mathbb{R}^2, \, t \in \mathbb{R},\\ u(
Externí odkaz:
http://arxiv.org/abs/2407.13074
Autor:
Mezher, Ali
This paper is focused on the modified Zakharov-Kusnetsov equation. We prove the associated Cauchy problem is locally (in time) well-posed in $H^s(\R \times \T)$ for $s >1$. The new ingredient in this work is a trilinear estimate in the context of Bou
Externí odkaz:
http://arxiv.org/abs/2407.04850
Autor:
Ban, Yingzhe, Shan, Minjie
We illustrate the dispersive blow up phenomena of the solutions of three dimensional generalized Zakharov-Kuznetsov equations. In particular, we construct smooth initial data such that, the associated global solutions fail to be $C^{1}$ at time $t$ i
Externí odkaz:
http://arxiv.org/abs/2408.14737
Autor:
Krieger, Joachim, Schmid, Tobias
Based on our companion paper [Krieger-Schmid, 2024], we show that the 4D energy critical Zakharov system admits finite time type II blow up solutions. The main new difficulty this work deals with is the appearance of a term in the linearization aroun
Externí odkaz:
http://arxiv.org/abs/2407.19972
Autor:
Krieger, Joachim, Schmid, Tobias
We construct approximate solutions $ (\psi_*, n_*)$ of the critical 4D Zakharov system which collapse in finite time to a singular renormalization of the solitary bulk solutions $ (\lambda e^{i \theta}W, \lambda^2 W^2)$ . To be precise for $ N \in \m
Externí odkaz:
http://arxiv.org/abs/2407.19971
In this article, we consider the Cauchy problem for the cubic (mass-critical) Zakharov-Kuznetsov equations in dimension two: $$\partial_t u+\partial_{x_1}(\Delta u+u^3)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}^{2}.$$ For initial data in $H^1$ clo
Externí odkaz:
http://arxiv.org/abs/2407.00300