Project description
How soliton waves behave over infinite time
Waves are often fleeting, spreading out and losing their intensity over time. Yet, in certain mathematical systems, solitary waves defy this norm, holding their shape and stability. These unique waves, known as solitons, are the focus of the ERC-funded INSOLIT project. Targeting topological solitons – namely kinks and rational maps inspired by quantum field theory – the proposed research aims to unravel their long-term behaviour and interactions. The goal is to understand how solitons evolve and also explore their collisions, stability and the subtle interplay between waves and radiation. The research will offer a more universal picture of soliton dynamics, which could be applied to a wide range of mathematical and physical systems.
Objective
Various models encountered in mathematical physics possess special solutions called solitary waves, which preserve their shape as
time passes. In the case of dispersive models, small perturbations of the field tend to spread, so that their amplitude decays. The
Soliton Resolution Conjecture predicts that, generically, a solution of a nonlinear dispersive partial differential equation decomposes
into a superposition of solitary waves and a perturbation of small amplitude called radiation.
Our study will focus on topological solitons appearing in models motivated by Quantum Field Theory: kinks in the phi4 theory and
rational maps in the O(3) sigma model. We expect that the developed techniques will have applications in the study of other
topological solitons like vortices, monopoles, Skyrmions and instantons.
Our general ultimate objective goes beyond the Soliton Resolution, and consists in obtaining an asymptotic description in infinite
time, in both time directions, of solutions of the considered model. Such a description should be correct at least at main order, and
reflect interesting features of the problem, which are the soliton-soliton interactions and soliton-radiation interactions.
We pursue this general goal in various concrete situations, namely: the problem of unique continuation after blow-up for the
equivariant wave maps equation, the collision problem for the phi4 equation, the study of pure multi-solitons in the regime of strong
interaction, and the multi-soliton uniqueness and stability problem. Their solution requires a mixture of non-perturbative and perturbative
techniques. While the former rely heavily on the concrete model, the latter will be applicable to any dispersive equation having
solitary waves.
Fields of science (EuroSciVoc)
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CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been human-validated.
Keywords
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2023-STG
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75006 Paris
France
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