Characteristics and the initial value problem of a completely integrable shallow water equation
Roberto Camassa - Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States (email)
Abstract: 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.
Keywords: Completely integrable systems, Hamiltonian structures, lattice
Received: March 2002; Revised: September 2002; Available Online: November 2002.
2015 Impact Factor1.227