Asymptotic solutions for singularly perturbed Boussinesq equations
Abbreviated Journal Title
Appl. Math. Comput.
Singularly perturbed Boussinesq equation; Weak solutions; Rational; solutions; Asymptotic series; SHALLOW-WATER EQUATION; Mathematics, Applied
We consider a family of singularly perturbed Boussinesq equations. We obtain a rational weak solution to the classical Boussinesq equation and demonstrate that this solution can be used to construct perturbation solutions for singularly perturbed high-order Boussinesq equations. These solutions take the form of an algebraic function which behaves similarly to a peakon, and which decays as time becomes large. We show that approximate solutions obtained via perturbation for the singularly perturbed models are asymptotic to the true solutions as the residual errors rapidly decay away from the origin. Published by Elsevier Inc.
Applied Mathematics and Computation
"Asymptotic solutions for singularly perturbed Boussinesq equations" (2012). Faculty Bibliography 2010s. 2727.