Description and Classification of 2-Solitary Waves for Nonlinear Damped Klein–Gordon Equations

Côte, Raphaël; Martel, Yvan; Yuan, Xu; Zhao, Liu

doi:10.1007/s00220-021-04241-5

Cited by 4 publications

(2 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

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

Kenjiro

Nakanishi

2022

Ann. PDE

View full text Add to dashboard Cite

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.

show abstract

Section: Previous Resultsmentioning

confidence: 99%

“…Second We recall properties of soliton interactions. In detail, see [8]. Before we establish the lemma about soliton interactions, we define some notations.…”

mentioning

confidence: 99%

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

Kenjiro

Nakanishi

2022

Ann. PDE

View full text Add to dashboard Cite

show abstract

Strongly interacting solitary waves for the fractional modified Korteweg-de Vries equation

Eychenne,

Valet

2023

Journal of Functional Analysis

View full text Add to dashboard Cite

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

Côte¹,

Yuan²

2022

Nonlinear Analysis

View full text Add to dashboard Cite

Description and Classification of 2-Solitary Waves for Nonlinear Damped Klein–Gordon Equations

Cited by 4 publications

References 30 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

Strongly interacting solitary waves for the fractional modified Korteweg-de Vries equation

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

Contact Info

Product

Resources

About