On asymptotic stability of multi-solitons for the focusing modified Korteweg-de Vries equation (Q6191537)

scientific article; zbMATH DE number 7814547

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English	On asymptotic stability of multi-solitons for the focusing modified Korteweg-de Vries equation	scientific article; zbMATH DE number 7814547

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title

On asymptotic stability of multi-solitons for the focusing modified Korteweg-de Vries equation (English)

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7 March 2024

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zbMATH Keywords

modified Korteweg-de Vries equation

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$\bar{\partial}$-steepest descent method

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dressing-up transformation

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multi-solitons

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asymptotic stability

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MaRDI profile type

MaRDI publication profile

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cites work

Q3342896

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Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋

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Introduction to nonlinear dispersive equations

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Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle

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Q4254645

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Asymptotic stability of solitons for mKdV

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Long time behavior of solutions to the mKdV

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Scattering and inverse scattering for first order systems

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L2-Sobolev space bijectivity of the scattering and inverse scattering transforms

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Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space

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Dispersive Asymptotics for Linear and Integrable Equations by the ∂ ¯ $$\overline {\partial }$$ Steepest Descent Method

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Asymptotic solutions of nonlinear evolution equations and a Painlevé transcedent

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A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation

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Riemann–Hilbert problem to the modified Korteveg–de Vries equation: Long-time dynamics of the steplike initial data

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Painlevé-type asymptotics of an extended modified KdV equation in transition regions

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Focusing and defocusing mKdV equations with nonzero boundary conditions: inverse scattering transforms and soliton interactions

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Soliton resolution for the focusing modified KdV equation

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Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces

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On the Cauchy problem of defocusing mKdV equation with finite density initial data: long time asymptotics in soliton-less regions

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Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data

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Stability of multi-solitons in the cubic NLS equation

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The asymptotic stability of solitons in the cubic NLS equation on the line

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The Formula steepest descent method and the asymptotic behavior of polynomials orthogonal on the unit circle with fixed and exponentially varying nonanalytic weights

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The Steepest Descent Method for Orthogonal Polynomials on the Real Line with Varying Weights

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Long time asymptotic behavior of the focusing nonlinear Schrödinger equation

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Soliton resolution for the derivative nonlinear Schrödinger equation

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Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data

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Soliton resolution for the short-pulse equation

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Long-time asymptotic behavior for the derivative Schrödinger equation with finite density type initial data

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Defocusing NLS equation with nonzero background: large-time asymptotics in a solitonless region

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On the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regions

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Soliton resolution and large time behavior of solutions to the Cauchy problem for the Novikov equation with a nonzero background

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On the soliton resolution and the asymptotic stability of $N$-soliton solution for the Wadati-Konno-Ichikawa equation with finite density initial data in space-time solitonic regions

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The defocusing nonlinear Schrödinger equation with a nonzero background: Painlevé asymptotics in two transition regions

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Q3779084

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.PHYSD.2023.134046

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Mathematics(1 entry)

mardi Publication:6191537