Analytical and numerical aspects of the solutions of nonlinear pde's modelling small amplitude, long water waves

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Project objective

The proposed research project has as main subject the theoretical and numerical investigation of some partial differential equations (pde) and of systems of pde's, which model water wave propagation. For some of these pde's there are many analytic results, based on the inverse scattering method; for other, this method is either not applicable, or the results one obtains are not satisfactory. We want to improve the existing analytic theory, using as guideline some new results and the outcome of recent numerical experiments, and to extend the inverse spectral method in cases for which the results obtained are so far very partial. It is very important to have good numerical methods to analyze the behaviour of the solutions of these model equations? and to derive evidence of the existence of the so-called solitary wave solutions; hence we want to continue the numerical investigation, improving the existing methods and analyzing rigorously their convergence properties.

Original text from CORDIS.

Participants

• IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE · LONDONCoordinatorUnited Kingdom
• Not availableCity levelItaly

Links

• View on CORDIS