首页/论文/2406.02423

arXiv 2406.024232024-06-04math.AP

CH-KP-I方程的周期调制孤立波

Periodically modulated solitary waves of the CH-KP-I equation

Dag Nilsson, Douglas Svensson Seth, Yuexun Wang

备注：: 11 pages

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

摘要英文摘要相关论文

AI总结：

本文研究CH-KP-I方程，证明了在一个水平方向孤立而在另一方向周期的稳态解的存在性，揭示了其从线孤立波解经维度破缺分岔产生，核心方法是将问题转化为扰动动力系统并应用Lyapunov-Iooss定理。

摘要：

我们考虑CH-KP-I方程。对于该方程，我们证明了稳态解的存在性，这些解在一个水平方向上是孤立的，而在另一个方向上是周期的。我们表明，此类波是从线孤立波解（即Camassa-Holm方程的孤立波解）通过维度破缺分岔产生的。这是通过将问题重新表述为线孤立波解的扰动的动力系统（其中周期方向扮演时间的角色），然后应用Lyapunov-Iooss定理来实现的。

英文摘要：

We consider the CH-KP-I equation. For this equation we prove the existence of steady solutions, which are solitary in one horizontal direction and periodic in the other. We show that such waves bifurcate from the line solitary wave solutions, i.e. solitary wave solutions to the Camassa-Holm equation, in a dimension-breaking bifurcation. This is achieved through reformulating the problem as a dynamical system for a perturbation of the line solitary wave solutions, where the periodic direction takes the role of time, then applying the Lyapunov-Iooss theorem.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

摘要英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Solitary waves in a Whitham equation with small surface tension

Using a nonlocal version of the center manifold theorem and a normal form reduction, we prove the existence of small-amplitude generalized solitary-wave solutions and modulated solitary-wave solutions to the steady gravity-capillary Whitham equation with weak surface tension. Through the application of the center manifold theorem, the nonlocal equation for the solitary wave profiles is reduced to a four-dimensional system of ODEs inheriting reversibility. Along particular parameter curves, relating directly to the classical gravity-capillary water wave problem, the associated linear operator i…

2021-09-23math.AP

Traveling waves and transverse instability for the fractional Kadomtsev-Petviashvili equation

Of concern are traveling wave solutions for the fractional Kadomtsev--Petviashvili (fKP) equation. The existence of periodically modulated solitary wave solutions is proved by dimension breaking bifurcation. Moreover, the line solitary wave solutions and their transverse (in)stability are discussed. Analogous to the classical Kadmomtsev--Petviashvili (KP) equation, the fKP equation comes in two versions: fKP-I and fKP-II. We show that the line solitary waves of fKP-I equation are transversely linearly instable. We also perform numerical experiments to observe the (in)stability dynamics of line…

2022-03-24math.AP

Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities

A nonlinear Schrödinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises naturally in modeling fiber-optics communication systems with periodically varying dispersion profile (dispersion management). The associated constrained variational principle is shown to posses a ground state solution by constructing a convergent minimizing sequence through the application of a method similar to the classical concentration compactness principle of Lions. One of the obstacles in applying this variational…

2017-07-21math.AP

$\mathbb{R}^3$中周期调制漏丝谱的绝对连续性

Absolute continuity of the spectrum for periodically modulated leaky wires in $\mathbb{R}^3$

我们考虑一个三维的漏量子线模型。哈密顿量是拉普拉斯算子的一个奇异扰动，它由一条耦合有界的直线支撑，并沿直线周期性地调制。我们证明了这样一个系统有一个纯粹的绝对连续的频谱和它的负部分的能带结构，最多有有限数量的差距。这一结果也被推广到当有无限多条线支持沿一个方向周期性排列的扰动时的情形。

2005-08-26math-phmath.APmath.MP

等效方程用于具有周期性变化横截面的等熵气体

Homogenized Equations for Isentropic Gas in a Pipe with Periodically-Varying Cross-Section

Imam Abdulrahman Bin Faisal University（伊玛目阿卜杜勒拉赫曼·本·费萨尔大学）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）

研究等熵气体在周期性变化横截面管道中的行为，通过多尺度扰动理论推导等效方程，包含色散高阶导数项，并提供近似黎曼求解器，比较原方程组与等效方程组的数值解，发现解呈现孤立波而非激波。

2026-04-18math.AP

Existence of Davey--Stewartson type solitary waves for the fully dispersive Kadomtsev--Petviashvilii equation

We prove existence of small-amplitude modulated solitary waves for the full-dispersion Kadomtsev--Petviashvilii (FDKP) equation with weak surface tension. The resulting waves are small-order perturbations of scaled, translated and frequency-shifted solutions of a Davey--Stewartson (DS) type equation. The construction is variational and relies upon a series of reductive steps which transform the FDKP functional to a perturbed scaling of the DS functional, for which least-energy ground states are found. We also establish a convergence result showing that scalings of FDKP solitary waves converge …

2021-10-08math.AP

更多相关论文收起更多论文

Zakharov-Kuznetsov方程两个近似相等孤立波碰撞的动力学

Dynamics of the collision of two nearly equal solitary waves for the Zakharov-Kuznetsov equation

研究2维和3维Zakharov-Kuznetsov方程中两个近似等速孤立波碰撞的动力学，通过构造近似解、修正能量泛函和精细调制估计证明了解的稳定性。

2024-03-04math.AP

Modulated equations of Hamiltonian PDEs and dispersive shocks

Motivated by the ongoing study of dispersive shock waves in non integrable systems, we propose and analyze a set of wave parameters for periodic waves of a large class of Hamiltonian partial differential systems -- including the generalized Korteweg de Vries equations and the Euler-Korteweg systems -- that are well-behaved in both the small amplitude and small wavelength limits. We use this parametrization to determine fine asymptotic properties of the associated modulation systems, including detailed descriptions of eigenmodes. As a consequence, in the solitary wave limit we prove that modula…

2020-11-20math.AP

On asymptotic dynamics for $L^2$ critical generalized KdV equations with a saturated perturbation

In this paper, we consider the $L^2$ critical gKdV equation with a saturated perturbation: $\partial_t u+(u_{xx}+u^5-γu|u|^{q-1})_x=0$, where $q>5$ and $0<γ\ll1$. For any initial data $u_0\in H^1$, the corresponding solution is always global and bounded in $H^1$. This equation has a family of solitons, and our goal is to classify the dynamics near soliton. Together with a suitable decay assumption, there are only three possibilities: (i) the solution converges asymptotically to a solitary wave, whose $H^1$ norm is of size $γ^{-2/(q-1)}$, as $γ\rightarrow0$; (ii) the solution is always in a sma…

2017-09-04math.AP

可压缩欧拉方程中的孤立波形成

Solitary wave formation in the compressible Euler equations

King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；University of Catania（卡塔尼亚大学）

通过渐近分析和计算实验，研究一维可压缩无粘气体中长波扰动近似服从色散非线性波动方程，并发现中等振幅初始数据下主要形成孤立波而避免激波，验证了过渡阈值准则。

2026-05-31math.APnlin.PSphysics.flu-dyn

Modulation analysis of the stochastic Camassa-Holm equation with pure jump noise

We study the stochastic Camassa-Holm equation with pure jump noise. We prove that if the initial condition of the solution is a solitary wave solution of the unperturbed equation, the solution decomposes into the sum of a randomly modulated solitary wave and a small remainder. Moreover, we derive the equations for the modulation parameters and show that the remainder converges to the solution of a stochastic linear equation as amplitude of the jump noise tends to zero.

2023-03-09math.APmath.PR

A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schrödinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength t…

2016-09-08math-phmath.APmath.MP

时间调制亚波长谐振器的散射

Scattering from time-modulated subwavelength resonators

研究时间调制高对比度亚波长谐振器系统的波散射问题，通过证明亚波长共振准频率的高阶离散电容矩阵近似并进行数值实验，揭示了周期性时变材料参数对散射波场的影响。

2024-01-02cs.NAmath-phmath.AP