Homoclinic solutions for fourth order traveling wave equations

2009/04/21 by Sanjiban Santra, Juncheng Wei, Santra, Sanjiban +1
Mathematics · Physics and Astronomy · #34B15 #34B60 #34E18 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0904.3147

openalex publication_date 2009/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider homoclinic solutions of fourth order equations u^"" + β² u^" + V_u (u)=0 in \R , where V(u) is either the suspension bridge type V(u)=e^u-1-u or Swift-Hohenberg type V(u)= 1/4(u²-1)². For the suspension bridge type equation, we prove existence of a homoclinic solution for \em all β∈ (0, β_*) where β_*= 0.7427.... For the Swift-Hohenberg type equation, we prove existence of a homoclinic solution for each β∈ (0, β_*), where β_*=0.9342.... This partially solves a conjecture of Chen--McKenna \citeYCM1.

Citations

• The existence of surfaces of constant mean curvature with free boundaries

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