Construction of non-analytic solutions for the generalized KdV equation

DOI10.1016/j.jmaa.2004.08.055zbMath1066.35088OpenAlexW2059573602MaRDI QIDQ1770991

A. Alexandrou Himonas, Jennifer Gorsky

Publication date: 7 April 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.08.055

zbMATH Keywords

Cauchy problemAnalytic initial dataCauchy estimates

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Solutions to PDEs in closed form (35C05)

Related Items (13)

Analyticity in partial differential equations ⋮ Well-posedness and regularity of the generalized Burgers equation in periodic Gevrey spaces ⋮ Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems ⋮ Gevrey regularity of the periodic gKdV equation ⋮ Unnamed Item ⋮ Formal solutions of semilinear heat equations ⋮ Real-valued non-analytic solutions for the generalized Korteweg-de Vries equation ⋮ Global analyticity for a generalized Camassa-Holm equation and decay of the radius of spatial analyticity ⋮ Analytic well-posedness of periodic gKdV ⋮ Radius of analyticity and exponential convergence for spectral projections of the generalized KdV equation ⋮ Unnamed Item ⋮ New traveling wave solutions and interesting bifurcation phenomena of generalized KdV-mKdV-like equation ⋮ SOME COMMON EXPRESSIONS AND NEW BIFURCATION PHENOMENA FOR NONLINEAR WAVES IN A GENERALIZED mKdV EQUATION

Cites Work

• Unnamed Item
• Unnamed Item
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Nonlinear evolution equations and analyticity. I
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• Analyticity of the Cauchy problem for an integrable evolution equation
• Exponential decay of the power spectrum of turbulence.
• Nonanalytic solutions of the KdV equation
• Multilinear estimates for periodic KdV equations, and applications
• A remark on time-analyticity for the Kuramoto--Sivashinsky equation
• Non-analyticity in time of solutions to the KdV equation
• Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
• Analyticity and smoothing effect for the Korteweg de Vries equation with a single point singularity
• SPATIAL ANALYTICITY PROPERTIES OF NONLINEAR WAVES
• Analyticity of Solutions of the Korteweg–De Vries Equation
• The inverse problem for periodic potentials
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Approximation of Attractors by Algebraic or Analytic Sets
• An integrable shallow water equation with peaked solitons
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• A bilinear estimate with applications to the KdV equation

This page was built for publication: Construction of non-analytic solutions for the generalized KdV equation