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pro vyhledávání: '"35Q51"'
We study the spectral stability of smooth, small-amplitude periodic traveling wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearities. Specifically, we investigate the $L^2(\mathbb{R})$-spectrum of the
Externí odkaz:
http://arxiv.org/abs/2409.13969
Publikováno v:
Chaos 34, 072104 (2024)
We present the fascinating phenomena of resonant radiation emitted by transient rogue waves in cubic and quadratic nonlinear media, particularly those shed from Peregrine solitons, one of the main wavepackets used today to model real-world rogue wave
Externí odkaz:
http://arxiv.org/abs/2411.04891
We examine the solution of the Benjamin-Ono Cauchy problem for rational initial data in three types of double-scaling limits in which the dispersion tends to zero while simultaneously the independent variables either approach a point on one of the tw
Externí odkaz:
http://arxiv.org/abs/2410.21581
The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in $L^2(\mathbb{R})$ is obtained explicitly for generic rational initial data $u_0$. An explicit asymptotic wave profile $u^\mathr
Externí odkaz:
http://arxiv.org/abs/2410.17405
We show that the initial-value problem for the Benjamin-Ono equation on $\mathbb{R}$ with $L^2(\mathbb{R})$ rational initial data with only simple poles can be solved in closed form via a determinant formula involving contour integrals. The dimension
Externí odkaz:
http://arxiv.org/abs/2410.14870
We investigate the dynamics arising out of the propagation of light pulses with different polarizations through a condensate (referred to as a constant background field) with cross coupling described by a coupled nonlinear Schrodinger equation(NLSE)
Externí odkaz:
http://arxiv.org/abs/2409.19233
We consider soliton gas solutions of the Focusing Nonlinear Schr\"odinger (NLS) equation, where the point spectrum of the Zakharov-Shabat linear operator condensate in a bounded domain $\mathcal{D}$ in the upper half-plane. We show that the correspon
Externí odkaz:
http://arxiv.org/abs/2409.14825
Autor:
Naz, Rehana, Hereman, Willy
The Lie-point symmetry method is used to find some closed-form solutions for a constitutive equation modeling stress in elastic materials. The partial differential equation (PDE), which involves a power law with arbitrary exponent n, was investigated
Externí odkaz:
http://arxiv.org/abs/2409.15593
Autor:
Magnot, Jean-Pierre, Reyes, Enrique G.
We start from the classical Kadomtsev-Petviashvili hierarchy posed on formal pseudo-differential operators, and we produce two hierarchies of non-linear equations posed on non-formal pseudo-differential operators lying in the Kontsevich and Vishik's
Externí odkaz:
http://arxiv.org/abs/2409.13771
In this paper, modified Toda (mToda) equation is generalized to form an integrable hierarchy in the framework of Sato theory, which is therefore called mToda hierarchy. Inspired by the fact that Toda hierarchy is 2--component generalization of usual
Externí odkaz:
http://arxiv.org/abs/2408.09450