From finite-gap solutions of KdV in terms of theta functions to solitons and positons

The scaling coefficients of the higher order time variables are explicitly computed in terms of the physical parame- ters, showing that the KdV asymptotic is valid only when the

Explicit examples of smooth, complex–valued solutions defined for x, t ∈ R of the Korteweg–de Vries equation (1.2) that blow up in finite time have been given in [2, 9, 15, 19]..

The time scaling coefficients studied in the previous section have given an insight into the convergence of the perturbative expansion as an asymptotic behaviour for small values of

When considering propagation times with an order of mag- nitude larger than 1/ε 3 , these secularities must be removed, and this is achieved, according to the mul- tiple time

In Section 9 we first compute the asymptotics of the Casimir functionals of the Toda lattice (Proposition 9.1) and then, using Theorem 2.1, obtain the asymptotics of the discriminant

This paper concerns the inverse problem of retrieving the principal coefficient in a Korteweg-de Vries (KdV) equation from boundary measurements of a single solution.. The

Optimal decay and asymptotic behavior of solutions to a non-local perturbed KdV equation.. Manuel Fernando Cortez,

Sanz-Serna and Christi di- vis d a modified Petrov-Galerkin finite elem nt method, and compared their method to the leading methods that had been developed to date: