Asymptotics of solutions with a compactness property for the nonlinear damped Klein–Gordon equation

Côte, Raphaël; Yuan, Xu

doi:10.1016/j.na.2021.112768

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“…To the best of our knowledge, this is the first complete proof of the soliton resolution conjecture for a non-integrable equation without any size or symmetry restriction and with moving solitons. Other results for the damped nonlinear Klein-Gordon equation are in [8,10,23]. Their arguments are useful for (DNKG).…”

Section: Previous Resultsmentioning

confidence: 99%

Global Dynamics Around 2-Solitons for the Nonlinear Damped Klein-Gordon Equations

Kenjiro

Nakanishi

2022

Ann. PDE

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We consider the damped nonlinear Klein-Gordon equation with a delta potential, where p > 2, α > 0, γ < 2, and δ 0 = δ 0 (x) denotes the Dirac delta with the mass at the origin. When γ = 0, Côte, Martel and Yuan [7] proved that any global solution either converges to 0 or to the sum of K ≥ 1 decoupled solitary waves which have alternative signs. In this paper, we first prove that any global solution either converges to 0 or to the sum of K ≥ 1 decoupled solitary waves. Next we construct a single solitary wave solution that moves away from the origin when γ < 0 and construct an even 2-solitary wave solution when γ ≤ −2. Last we give single solitary wave solutions and even 2-solitary wave solutions an upper bound for the distance between the origin and the solitary wave.

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Section: Previous Resultsmentioning

confidence: 99%

Global Dynamics Around 2-Solitons for the Nonlinear Damped Klein-Gordon Equations

Kenjiro

Nakanishi

2022

Ann. PDE

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Long-time asymptotics of the damped nonlinear Klein–Gordon equation with a delta potential

Ishizuka

2025

Nonlinear Analysis

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Asymptotics of solutions with a compactness property for the nonlinear damped Klein–Gordon equation

Cited by 2 publications

References 23 publications

Global Dynamics Around 2-Solitons for the Nonlinear Damped Klein-Gordon Equations

Global Dynamics Around 2-Solitons for the Nonlinear Damped Klein-Gordon Equations

Long-time asymptotics of the damped nonlinear Klein–Gordon equation with a delta potential

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