Stability of the line soliton of the KP-II equation under periodic transverse perturbations

DOI10.1007/s00208-011-0654-3zbMath1233.35174arXiv1008.0812OpenAlexW1991406046MaRDI QIDQ662399

Tetsu Mizumachi, Nickolay Tzvetkov

Publication date: 22 February 2012

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.0812

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton solutions (35C08)

Related Items

Breather solutions of a negative order modified Korteweg-de Vries equation and its nonlinear stability ⋮ Global well-posedness of partially periodic KP-I equation in the energy space and application ⋮ Transverse stability issues in Hamiltonian PDE ⋮ Counting unstable eigenvalues in Hamiltonian spectral problems via commuting operators ⋮ On the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system ⋮ The Cauchy Problem for the Fractional Kadomtsev--Petviashvili Equations ⋮ Stability of line solitons for the KP-II equation in ℝ² ⋮ Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations ⋮ A semi-periodic initial-value problem for the Kadomtsev–Petviashvili II equation ⋮ Linear stability of elastic 2-line solitons for the KP-II equation ⋮ Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ The Phase Shift of Line Solitons for the KP-II Equation ⋮ Asymptotic linear stability of Benney–Luke line solitary waves in 2D ⋮ Stability and instability of the KdV solitary wave under the KP-I flow ⋮ Stability of Benney--Luke Line Solitary Waves in 2 Dimensions ⋮ Global well-posedness for the KP-II equation on the background of a non-localized solution ⋮ Stability for line solitary waves of Zakharov-Kuznetsov equation ⋮ The Gardner equation and the 𝐿²-stability of the 𝑁-soliton solution of the Korteweg-de Vries equation ⋮ Transverse instability of the line solitary water-waves ⋮ Orbital stability and asymptotic stability of mKdV breather-type soliton solutions ⋮ Transverse instability of periodic and generalized solitary waves for a fifth-order KP model ⋮ Transverse linear stability of line periodic traveling waves for water-wave models ⋮ Nondegeneracy, Morse index and orbital stability of the KP-I lump solution ⋮ Transverse Instability of the CH-KP-I Equation ⋮ \(L^2\)-stability of multi-solitons

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global well-posedness for the KP-II equation on the background of a non-localized solution
• Asymptotic stability of lattice solitons in the energy space
• Global well-posedness of the KP-I initial-value problem in the energy space
• Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941]
• Degenerative dispersion laws, motion invariants and kinetic equations
• Transverse nonlinear instability for two-dimensional dispersive models
• On KP-II type equations on cylinders
• Inverse scattering for the heat operator and evolutions in \(2+1\) variables
• On the asymptotic behavior of solutions to the (generalized) Kadomtsev-Petviashvili-Burgers equations
• On the Cauchy problem for the Kadomtsev-Petviashvili equation
• Non existence of \(L^2\)-compact solutions of the Kadomtsev-Petviashvili II equation
• A Liouville theorem for the critical generalized Korteweg-de Vries equation
• Global well-posedness for the Kadomtsev-Petviashvili II equation
• Global well-posedness for the KP-I equation on the background of a non-localized solution
• Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's
• LOCAL AND GLOBAL CAUCHY PROBLEMS FOR THE KADOMTSEV–PETVIASHVILI (KP–II) EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES
• Solitary waves on FPU lattices: II. Linear implies nonlinear stability
• Global well-posedness in the energy space for a modified KP II equation via the Miura transform
• Asymptotic stability of Toda lattice solitons
• Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations
• On the stability theory of solitary waves
• Solitary waves on Fermi–Pasta–Ulam lattices: III. Howland-type Floquet theory
• Solitary waves on Fermi–Pasta–Ulam lattices: IV. Proof of stability at low energy
• On the initial value problem for the KPII equation with data that do not decay along a line
• Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
• On asymptotic stability in 3D of kinks for the 𝜙⁴ model
• Remarks on the Mass Constraint for KP-Type Equations
• Global low-regularity solutions for Kadomtsev-Petviashvili equation