Existence of multi-solitons with any parameters for the 5D energy critical wave equation

2025/10/22 by Yvan Martel, Martel, Yvan, Frank Merle +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2510.19609

openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

For the focusing, energy critical wave equation in dimension 5, we construct multi-solitons with any number of solitons, any choice of signs, speeds, scaling parameters and translation parameters. This requires to revisit in depth previous constructions of multi-solitons based on a unidirectional approach, to fully take into account the dimension of the space and the possibility for solitons to move in any direction. Then, as a consequence of this more general construction and of the arguments developed in a previous article, the inelastic nature of any collision of solitons is proved under a non-cancellation assumption on the parameters.

Citations

• Soliton resolution for energy-critical wave maps in the equivariant case
• Construction of excited multi-solitons for the focusing 4D cubic wave equation
• Construction of excited multi-solitons for the 5D energy-critical wave\n equation
• Soliton resolution for the radial critical wave equation in all odd space dimensions
• Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations
• Construction of two-bubble solutions for energy-critical wave equations
• Soliton resolution along a sequence of times for the focusing energy critical wave equation
• Channels of energy for the linear radial wave equation
• Solutions of the focusing nonradial critical wave equation with the compactness property
• Relaxation of wave maps exterior to a ball to harmonic maps for all data
• Multi-solitons for nonlinear Klein-Gordon equations
• Classification of radial solutions of the focusing, energy-critical wave equation
• Inelastic interaction of nearly equal solitons for the quartic gKdV equation
• Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation
• Construction of multi-soliton solutions for the L2-supercritical gKdV and NLS equations
• Description of two soliton collision for the quartic gKdV equation
• Global well-posedness, scattering and blow-up for the energy critical focusing non-linear wave equation
• Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations

Related

• Construction of multi-soliton solutions for the energy critical wave equation in dimension 3
• Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5
• Soliton resolution along a sequence of times for the focusing energy critical wave equation
• Construction of multi solitary waves with symmetry for the damped nonlinear Klein-Gordon equation
• Construction of excited multi-solitons for the 5D energy-critical wave\n equation