• Corpus ID: 235294080

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

@inproceedings{Friederich2021OnEA,
title={On existence and uniqueness of asymptotic \$N\$-soliton-like solutions of the nonlinear klein-gordon equation},
author={Xavier Friederich},
year={2021}
}
We are interested in solutions of the nonlinear Klein-Gordon equation (NLKG) in R1+3, 3 ≥ 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 # -parameter family of solutions of (NLKG) which converges exponentially fast to a sum of # given (unstable) solitons. For # = 1, this family completely describes the set of solutions…

## References

SHOWING 1-10 OF 33 REFERENCES
Multi-solitons for nonlinear Klein–Gordon equations
• Mathematics
Forum of Mathematics, Sigma
• 2014
Abstract In this paper, we consider the existence of multi-soliton structures for the nonlinear Klein–Gordon (NLKG) equation in $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le Multi-Soliton Solutions for the Supercritical gKdV Equations For the L 2 subcritical and critical (gKdV) equations, Martel [11] proved the existence and uniqueness of multi-solitons. Recall that for any N given solitons, we call multi-soliton a solution of Asymptotic N-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations <abstract abstract-type="TeX"><p>We consider the generalized Korteweg-de Vries equations <div class="disp-formula" id="df01" xmlns:m="http://www.w3.org/1998/Math/MathML" Multi-travelling waves for the nonlinear Klein-Gordon equation • Mathematics Transactions of the American Mathematical Society • 2018 For the nonlinear Klein-Gordon equation in R 1 + d \mathbb {R}^{1+d} , we prove the existence of multi-solitary waves made of any number N N of decoupled bound Construction of Multi-Solitons for the Energy-Critical Wave Equation in Dimension 5 • Mathematics • 2015 AbstractWe construct 2-solitons of the focusing energy-critical nonlinear wave equation in space dimension 5, that is solutions $${u}$$u of the equation such that$$u(t) - \left[ W_1(t) + Multi-existence of multi-solitons for the supercritical nonlinear Schr\ For the L2 supercritical generalized Korteweg-de Vries equation, we proved in a previous article the existence and uniqueness of an N-parameter family of N-solitons. Recall that, for any N given Construction and characterization of solutions converging to solitons for supercritical gKdV equations We consider the generalized Korteweg-de Vries equation in the supercritical case, and we are interested in solutions which converge to a soliton in large time in H^1. In the subcritical case, such Dynamic of Threshold Solutions for Energy-Critical NlS • Physics, Mathematics • 2007 Abstract.We consider the energy-critical non-linear focusing Schrödinger equation in dimension N = 3, 4, 5. An explicit stationary solution, W, of this equation is known. In [KeM], the energy E(W) Dynamic of threshold solutions for energy-critical wave equation • Mathematics • 2007 We consider the energy-critical non-linear focusing wave equation in dimension N=3,4,5. An explicit stationnary solution,$W\$, of this equation is known. The energy E(W,0) has been shown by C. Kenig