On existence and uniqueness of asymptotic N-soliton-like solutions of the nonlinear klein-gordon equation

2021/06/02 by Xavier Friederich, Friederich, Xavier
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP

paper · pdf · doi:10.48550/arxiv.2106.01106

openalex publication_date 2021/06/02 · arxiv created 2021/06/17 · arxiv updated 2021/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are interested in solutions of the nonlinear Klein-Gordon equation (NLKG) in ℝ^1+d, d≥1, which behave as a soliton or a sum of solitons in large time. In the spirit of other articles focusing on the supercritical generalized Korteweg-de Vries equations and on the nonlinear Schrödinger equations, we obtain an N-parameter family of solutions of (NLKG) which converges exponentially fast to a sum of given (unstable) solitons. For N = 1, this family completely describes the set of solutions converging to the soliton considered; for N≥ 2, we prove uniqueness in a class with explicit algebraic rate of convergence.

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