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pro vyhledávání: '"35c08"'
Explicit solutions to the related integrable nonlinear evolution equations are constructed by solving the inverse scattering problem in the reflectionless case for the third-order differential equation $d^3\psi/dx^3+Q\,d\psi/dx+P\psi=k^3\psi,$ where
Externí odkaz:
http://arxiv.org/abs/2412.10971
Autor:
Kumar, C. Senthil, Radha, R.
Publikováno v:
Wave motion 133 (2025) 103456
In this paper, we analyse the (3+1) dimensional Bogoyavlensky - Konopelchenko equation. Using Painlev\'e Truncation approach, we have constructed solutions in terms of lower dimensional arbitrary functions of space and time. By suitably harnessing th
Externí odkaz:
http://arxiv.org/abs/2412.10333
The Klein-Gordon-Boussinesq (KGB) system is proposed in the literature as a model problem to study the validity of approximations in the long wave limit provided by simpler equations such as KdV, nonlinear Schr\"{o}dinger or Whitham equations. In thi
Externí odkaz:
http://arxiv.org/abs/2411.18173
We found two stationary solutions of the parametrically driven, damped nonlinear Schr\"odinger equation with nonlinear term proportional to $|\psi(x,t)|^{2 \kappa} \psi(x,t)$ for positive values of $\kappa$. By linearizing the equation around these e
Externí odkaz:
http://arxiv.org/abs/2411.17655
Autor:
Espinal, Maria Fernanda, Sáez, Mariel
In this paper we classify rotationally symmetric conformally flat admissible solitons to the $k$-Yamabe flow, a fully non-linear version of the Yamabe flow. For $n\geq 2k$ we prove existence of complete expanding, steady and shrinking solitons and de
Externí odkaz:
http://arxiv.org/abs/2410.06942
Publikováno v:
Journal of Differential Equations, Volume 419, 25 February 2025, Pages 291-323
We study an integrable equation whose solutions define a triad of one-forms describing a surface with Gaussian curvature -1. We identify a local group of diffeomorphisms that preserve these solutions and establish conserved quantities. From the symme
Externí odkaz:
http://arxiv.org/abs/2409.01537
We investigate the blow-up dynamics for the $L^2$ critical two-dimensional Zakharov-Kuznetsov equation \begin{equation*} \begin{cases} \partial_t u+\partial_{x_1} (\Delta u+u^3)=0, \mbox{ } x=(x_1,x_2)\in \mathbb{R}^2, \mbox{ } t \in \mathbb{R}\\ u(0
Externí odkaz:
http://arxiv.org/abs/2406.06568
Autor:
Song, Linjie, Zou, Wenming
We develop a new framework to prove the existence of two positive solutions with prescribed mass on star-shaped bounded domains: one is the normalized ground state and another is of M-P type. We merely address the Sobolev critical cases since the Sob
Externí odkaz:
http://arxiv.org/abs/2404.11204
We study the stability and dynamics of solitons in the Korteweg de-Vries (KdV) equation with small multiplicative forcing. Forcing breaks the conservative structure of the KdV equation, leading to substantial changes in energy over long time. We show
Externí odkaz:
http://arxiv.org/abs/2404.01755
Autor:
Valchev, T.
We consider a matrix nonlinear partial differential equation that generalizes Heisenberg ferromagnet equation. This generalized Heisenberg ferromagnet equation is completely integrable with a linear bundle Lax pair related to the pseudo-unitary algeb
Externí odkaz:
http://arxiv.org/abs/2403.18165