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pro vyhledávání: '"Fan, Engui"'
The Degasperis-Procesi (DP) equation \begin{align} &u_t-u_{txx}+3\kappa u_x+4uu_x=3u_x u_{xx}+uu_{xxx}, \nonumber \end{align} serving as an asymptotic approximation for the unidirectional propagation of shallow water waves, is an integrable model of
Externí odkaz:
http://arxiv.org/abs/2409.01505
We consider the Cauchy problem to the general defocusing and focusing $p\times q$ matrix nonlinear Schr\"{o}dinger (NLS) equations with initial data allowing arbitrary-order poles and spectral singularities. By establishing the $L^{2}$-Sobolev space
Externí odkaz:
http://arxiv.org/abs/2408.14709
In this article, we investigate some problems about the initial-value problem of the focusing Ablowitz-Ladik system, and the initial data belongs to a discrete weighted $\ell^2$ space. On the one hand, we have proved the global well-posedness for the
Externí odkaz:
http://arxiv.org/abs/2407.21526
In this paper, we establish the orbital stability of the 1-soliton solution for the derivative nonlinear Schr\"odinger equation under perturbations in $L^2(\mathbb{R})$. We demonstrate this stability by utilizing the B\"acklund transformation associa
Externí odkaz:
http://arxiv.org/abs/2402.16222
In this paper, we develop a Riemann-Hilbert (RH) approach to the Cauchy problem for the two-component modified Camassa-Holm (2-mCH) equation based on its Lax pair. Further via a series of deformations to the RH problem by using the $\bar{\partial}$-g
Externí odkaz:
http://arxiv.org/abs/2402.13620
In this paper, we investigate the large time asymptotic behavior in two transition zones for the solutions to the Cauchy problem of the Novikov equation under a nonzero background \begin{align} &u_{t}-u_{txx}+4 u_{x}=3uu_xu_{xx}+u^2u_{xxx}, \nonumber
Externí odkaz:
http://arxiv.org/abs/2310.19278
Autor:
Ma, Ruihong, Fan, Engui
The Ostrovsky-Vakhnenko (OV) equation \begin{align*} &u_{txx}-3\kappa u_x+3u_xu_{xx}+uu_{xxx}=0 \end{align*} is a short wave model of the well-known Degasperis-Procesi equation and admits a $3\times 3$ matrix Lax pair. In this paper, we study the sol
Externí odkaz:
http://arxiv.org/abs/2310.13657
Autor:
Wen, Lili, Fan, Engui
We consider the Cauchy problem for the defocusing complex mKdV equation with a finite density initial data \begin{align*} &q_t+\frac{1}{2}q_{xxx}-\left(|q|^2q\right)_{x}=0,\\ &q(x,0)=q_{0}(x) \sim \pm 1, \ x\to \pm\infty, \end{align*} which can be fo
Externí odkaz:
http://arxiv.org/abs/2308.02740
Autor:
Ma, Ruihong, Fan, Engui
In this paper, the $\overline\partial$-steepest descent method and B\"acklund transformation are used to study the asymptotic stability of solitons to the Cauchy problem of focusing Hirota equation. The solution of the RH problem is further decompose
Externí odkaz:
http://arxiv.org/abs/2308.00359
With $\bar{\partial}$-generalization of the Deift-Zhou steepest descent method, we investigate the long-time asymptotics of the solution to the Cauchy problem for the Hunter-Saxton (HS) equation \begin{eqnarray} &&u_{txx}-2\omega u_x+2u_xu_{xx}+uu_{x
Externí odkaz:
http://arxiv.org/abs/2307.16172