Nonlinear stability of multi-solitons for the Hirota equation
DOI10.1016/j.jde.2022.10.016zbMath1501.35330OpenAlexW4306818413MaRDI QIDQ2097021
Yamin Xiao, Zhong Wang, Bo-ling Guo
Publication date: 11 November 2022
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2022.10.016
PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Soliton solutions (35C08) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stability of Hasimoto solitons in energy space for a fourth order nonlinear Schrödinger type equation
- Stability of solitary waves for derivative nonlinear Schrödinger equation
- Orbital stability of double solitons for the Benjamin-Ono equation
- Stability theory of solitary waves in the presence of symmetry. II
- Orbital stability of standing waves for some nonlinear Schrödinger equations
- Multiple pole solutions of the nonlinear Schrödinger equation
- Stability theory of solitary waves in the presence of symmetry. I
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Global smooth solution for nonlinear evolution equation of Hirota type
- On the generalized Korteweg-de Vries type equations
- Well-posedness of the Cauchy problem for the Hirota equation in Sobolev spaces \(H^s\)
- Stability and asymptotic stability for subcritical gKdV equations
- Orbital stability of solitary waves for the nonlinear derivative Schrödinger equation
- Stability of smooth multi-solitons for the Camassa-Holm equation
- Orbital stability of KdV multisolitons in \(H^{-1}\)
- Isoinertial operators around the KdV multi-solitons
- Exact solutions of the Hirota equation and vortex filaments motion
- Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations
- Spectra of Linearized Operators for NLS Solitary Waves
- On the stability ofN-solitons in integrable systems
- Periodic solutions of the KdV equation
- On the stability theory of solitary waves
- A simple model of the integrable Hamiltonian equation
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- On the stability of KdV multi‐solitons
- THE CAUCHY PROBLEM FOR A THIRD ORDER NONLINEAR SCHRÖDINGER EQUATION
- Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
- Stability of multisolitons for the derivative nonlinear Schrödinger equation
- Stability of Periodic Waves of 1D Cubic Nonlinear Schrödinger Equations
- Eigenfunctions of Linearized Integrable Equations Expanded Around an Arbitrary Solution
- Stability and instability of breathers in the U(1) Sasa–Satsuma and nonlinear Schrödinger models*
- Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs
- Stability of the multi-solitons of the modified Korteweg–de Vries equation *
- New Exact Travelling Wave Solutions to Hirota Equation and (1+1)-Dimensional Dispersive Long Wave Equation
- A soliton on a vortex filament
- Exact envelope-soliton solutions of a nonlinear wave equation
- Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems