Stability of elliptic function solutions for the focusing modified KdV equation

DOI10.1016/j.aim.2023.109356arXiv2109.05454OpenAlexW4387889331MaRDI QIDQ6187711

Xuan Sun, Liming Ling

Publication date: 1 February 2024

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.05454

zbMATH Keywords

orbital stabilityspectral stabilitybreather solutionmKdV equationelliptic functionsubharmonic perturbations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Perturbations in context of PDEs (35B20) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Elliptic functions and integrals (33E05) Soliton solutions (35C08)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear stability of MKdV breathers
• The orbital stability of the cnoidal waves of the Korteweg-de Vries equation
• Computing spectra of linear operators using the Floquet-Fourier-Hill method
• Stability of small periodic waves for the nonlinear Schrödinger equation
• Nonlinear stability of periodic traveling wave solutions to the Schrödinger and the modified Korteweg-de Vries equations
• Stability theory of solitary waves in the presence of symmetry. II
• Stability of cnoidal waves
• On the spectra of periodic waves for infinite-dimensional Hamiltonian systems
• Stability of dnoidal waves to Hirota-Satsuma system.
• Stability and instability of periodic travelling wave solutions for the critical Korteweg-de Vries and nonlinear Schrödinger equations
• KdV cnoidal waves are spectrally stable
• Stability theory of solitary waves in the presence of symmetry. I
• Spectral and dynamical stability of nonlinear waves
• The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy.
• The stability spectrum for elliptic solutions to the focusing NLS equation
• Stability and interaction of compactons in the sublinear KdV equation
• Periodic standing waves in the focusing nonlinear Schrödinger equation: rogue waves and modulation instability
• Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background
• Theta vocabulary. I
• Orbital stability of periodic waves for the nonlinear Schrödinger equation
• Soliton dynamics in phase-modulated lattices
• The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation
• Nonlinear Waves in Integrable and Nonintegrable Systems
• An index theorem for the stability of periodic travelling waves of Korteweg–de Vries type
• Spectra of positive and negative energies in the linearized NLS problem
• Instabilities of Multihump Vector Solitons in Coupled Nonlinear Schrödinger Equations
• Algebraic construction of the Darboux matrix revisited
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Stability and instability of solitary waves of Korteweg-de Vries type
• Korteweg‐devries equation and generalizations. VI. methods for exact solution
• Periodic solutions of the KdV equation
• On the stability theory of solitary waves
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Rogue periodic waves of the focusing nonlinear Schrödinger equation
• Rogue periodic waves of the modified KdV equation
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• Orbital stability of a sum of solitons and breathers of the modified Korteweg–de Vries equation
• Multi‐breather and high‐order rogue waves for the nonlinear Schrödinger equation on the elliptic function background
• Elliptic solutions of the defocusing NLS equation are stable
• The Orbital Stability of Elliptic Solutions of the Focusing Nonlinear Schrödinger Equation
• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
• Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations
• Integrals of nonlinear equations of evolution and solitary waves
• Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
• On the spectrum of the periodic focusing Zakharov-Shabat operator