Validity of the weakly nonlinear solution of the cauchy problem for the boussinesq-type equation
journal contributionposted on 28.01.2016, 11:26 by Karima Khusnutdinova, Kieron R. Moore, Dmitry Pelinovsky
We consider the initial-value problem for the regularized Boussinesq-type equation in the class of periodic functions. Validity of the weakly nonlinear solution, given in terms of two counterpropagating waves satisfying the uncoupled Ostrovsky equations, is examined. We prove analytically and illustrate numerically that the improved accuracy of the solution can be achieved at the timescales of the Ostrovsky equation if solutions of the linearized Ostrovsky equations are incorporated into the asymptotic solution. Compared to the previous literature, we show that the approximation error can be controlled in the energy space of periodic functions and the nonzero mean values of the periodic functions can be naturally incorporated in the justification analysis. © 2014 by the Massachusetts Institute of Technology.
The research was supported by the LMS Scheme 2 grant and by the Loughborough University School of Science small grant.
- Mathematical Sciences