Large Time Asymptotics of Solutions Around Solitary Waves to the Generalized Korteweg--de Vries Equations
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Publication:2706224
DOI10.1137/S0036141098346827zbMath0981.35066OpenAlexW2066529622MaRDI QIDQ2706224
Publication date: 19 March 2001
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/s0036141098346827
Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)
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Asymptotic stability of high-dimensional Zakharov-Kuznetsov solitons ⋮ Asymptotic stability of solitons for mKdV ⋮ Asymptotic stability of the black soliton for the Gross–Pitaevskii equation ⋮ Soliton resolution for the focusing modified KdV equation ⋮ Long-term stability for KdV solitons in weighted \(H^s\) spaces ⋮ Stability for line solitary waves of Zakharov-Kuznetsov equation ⋮ Asymptotic stability of solitons of the gKdV equations with general nonlinearity ⋮ Dynamics near the solitary waves of the supercritical gKDV equations ⋮ Center stable manifolds around line solitary waves of the Zakharov-Kuznetsov equation with critical speed ⋮ A rigidity property for the Novikov equation and the asymptotic stability of peakons ⋮ On asymptotic stability of nonlinear waves ⋮ The structure of algebraic solitons and compactons in the generalized Korteweg-de Vries equation
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