# American Institute of Mathematical Sciences

February  2003, 3(1): 115-139. doi: 10.3934/dcdsb.2003.3.115

## Characteristics and the initial value problem of a completely integrable shallow water equation

 1 Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States

Received  March 2002 Revised  September 2002 Published  November 2002

The initial value problem for a completely integrable shallow water wave equation is analyzed through its formulation in terms of characteristics. The resulting integro-differential equations give rise to finite dimensional projections onto a class of distributional solutions of the equation, equivalent to taking the Riemann sum approximation of the integrals. These finite dimensional projections are then explicitly solved via a Gram-Schmidt orthogonalization procedure. A particle method based on these reductions is implemented to solve the wave equation numerically.
Citation: Roberto Camassa. Characteristics and the initial value problem of a completely integrable shallow water equation. Discrete & Continuous Dynamical Systems - B, 2003, 3 (1) : 115-139. doi: 10.3934/dcdsb.2003.3.115
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