NUMERICAL STUDY OF ELLIPTIC-HYPERBOLIC DAVEY–STEWARTSON SYSTEM: DROMIONS SIMULATION AND BLOW-UP
C. BESSE, C. H. BRUNEAU
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Source: Crossref
Published: Dec 1, 1998
DOI: 10.1142/s0218202598000640
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This paper is devoted to the numerical approximation of the elliptic-hyperbolic form of the Davey–Stewartson equations. A well-suited finite differences scheme that preserves the energy is derived. This scheme is tested to compute the famous dromion 1–1 and dromion 2–2 solutions. The accuracy of Crank–Nicolson scheme is discussed and it is shown that it induces a phase error. The qualitative behaviour of the solutions is then studied; in particular the influence of the initial datum and of the various parameters is pointed out. Finally, numerical experiments show the existence of blow-up solutions.
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