Project Grant 2407358

Award Date 8/1/24
Completion Date 7/31/27
Dollars Obligated $283K
Federal Grant Program
47.049
Assistance Type
Project Grant
Place of Performance
Urbana, IL 61801, USA
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This $282,599 project grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at the University of Illinois to study the stability of nonlinear waves using validated numerical methods. The key products include:

  • Rigorous mathematical analysis and computational techniques to establish the stability of special solutions, such as traveling waves, to nonlinear partial differential equations governing phenomena like ocean wave propagation and optical fiber dynamics. This work represents the first time the essential spectrum has been calculated rigorously for such operators arising from non-integrable equations.

  • Development of validated numerical methods, which provide mathematical proofs of solution correctness, to study the long-term dynamics and stability of linearized solutions. This approach will be extended to encompass a broader class of equations beyond the generalized KdV and nonlinear Schrödinger equations.

  • Training of graduate students in these increasingly important validated numerical techniques, which can be applied across a range of scientific and engineering disciplines.

The award period is from August 1, 2024 to July 31, 2027.

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