Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV Equation

Details Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV Equation Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV Equation

2006-08-30

arxiv.org/abs/nlin/0608066v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

32 pages, 1 figure

Scientific paper

We study the zero dispersion limit of the fifth order KdV equations when time is sufficiently large. In general, the weak limit may be described by an arbitrary odd number of hyperbolic equations. Unlike the KdV case, these are non-strictly hyperbolic equations. However, we show that the weak limit is governed by three hyperbolic equations in a domain in the space-time for all times bigger than a large time. Outside this domain, the weak limit satisfies a single hyperbolic equation.

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