Stability of KdV solitons on the half-line

DOI10.4171/rmi/1102OpenAlexW2969263469MaRDI QIDQ2280511

Claudio Muñoz, Márcio André Araújo Cavalcante

Publication date: 18 December 2019

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.02608

zbMATH Keywords

stabilitysolitonsKdVhalf-lines

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

Related Items (4)

Asymptotic Stability of KdV Solitons on the Half-Line: A Study in the Energy Space ⋮ Initial boundary value problems for some nonlinear dispersive models on the half-line: a review and open problems ⋮ Linear instability criterion for the Korteweg–de Vries equation on metric star graphs ⋮ Stability of mKdV breathers on the half-line

Cites Work

• Unnamed Item
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• The linear KdV equation with an interface
• Stability of integrable and nonintegrable structures
• Constrained energy minimization and orbital stability for the NLS equation on a star graph
• Global well-posedness of two initial-boundary-value problems for the Korteweg-de Vries equation.
• Well-posedness of the Cauchy problem for the Korteweg-de Vries equation at the critical regularity.
• Variational properties and orbital stability of standing waves for NLS equation on a star graph
• The Korteweg-de Vries equation in a quarter plane, continuous dependence results
• Global well-posedness of Korteweg-de Vries equation in \(H^{-3/4}(\mathbb R)\)
• Stability theory of solitary waves in the presence of symmetry. I
• Initial boundary-value problems for the Korteweg-de Vries equation
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• An initial-boundary value problem for the Korteweg-de Vries equation
• Nonlinear instability of half-solitons on star graphs
• On the ill-posedness of some canonical dispersive equations.
• Stability and asymptotic stability for subcritical gKdV equations
• On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
• Soliton dynamics for generalized KdV equations in a slowly varying medium
• The Korteweg-de Vries equation on a metric star graph
• Logarithmic NLS equation on star graphs: existence and stability of standing waves.
• Stability of standing waves for NLS-log equation with \(\delta\)-interaction
• Fast soliton scattering by delta impurities
• Conditional and unconditional well-posedness for nonlinear evolution equations
• Boundary smoothing properties of the Korteweg-de Vries equation in a quarter plane and applications
• A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane
• The Korteweg–de Vries equation on the half-line
• Ground State on the Dumbbell Graph
• FAST SOLITONS ON STAR GRAPHS
• The Korteweg–de Vries Equation, Posed in a Quarter-Plane
• Explicit soliton asymptotics for the Korteweg–de Vries equation on the half-line
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Stability and instability of solitary waves of Korteweg-de Vries type
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• A unified transform method for solving linear and certain nonlinear PDEs
• An Initial Boundary-Value Problem in a Half-Strip for the Korteweg–De Vries Equation in Fractional-Order Sobolev Spaces
• THE GENERALIZED KORTEWEG–DE VRIES EQUATION ON THE HALF LINE
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• A bilinear estimate with applications to the KdV equation
• The Gardner equation and the 𝐿²-stability of the 𝑁-soliton solution of the Korteweg-de Vries equation
• Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
• The Initial-Boundary Value Problem for the Korteweg–de Vries Equation
• Introduction to nonlinear dispersive equations

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