Construction of multi-solitons for the energy-critical wave equation in dimension 5

Abstract

We construct 2-solitons of any speed of the focusing energy-critical nonlinear wave equation in dimension 5. The existence result also holds for the case of K-solitons, for any K >2, assuming that the speeds are collinear. The main difficulty of the construction is the strong interaction between the solitons due to the slow spatial decay of the single soliton. This is in contrast with previous constructions of multi-solitons for other nonlinear models (like generalized KdV and nonlinear Schrodinger equations in energy subcritical cases), where the interactions are exponentially small in time due to the exponential decay of the solitons.

References in corpus (5)

• Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5
• Construction of multi-solitons for the energy-critical wave equation in dimension 5
• Strongly interacting blow up bubbles for the mass critical NLS
• Nonexistence of radial two-bubbles with opposite signs for the energy-critical wave equation
• Two soliton solutions to the three dimensional gravitational Hartree equation

Cited by in corpus (11)

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• Inelasticity of soliton collisions for the 5D energy critical wave equation
• Nonexistence of radial two-bubbles with opposite signs for the energy-critical wave equation
• Blow-up of a critical Sobolev norm for energy-subcritical and energy-supercritical wave equations
• An asymptotic expansion of two-bubble wave maps
• On multi-solitons for the energy-critical wave equation in dimension 5
• Multisolitons for the defocusing energy critical wave equation with potentials
• Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations
• Global, Non-scattering solutions to the quintic, focusing semilinear wave equation on ${\mathbb{R}}^{1+3}$
• Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity