Abstract
The problem addressed in this paper is the verification of numerical solutions of nonlinear dispersive wave equations such as Boussinesq-like system of equations. A practical verification tool for numerical results is to compare the numerical solution to an exact solution if available. In this work, we derive some exact solitary wave solutions and several invariants of motion for a wide range of Boussinesq-like equations using Maple software. The exact solitary wave solutions can be used to specify initial data for the incident waves in the Boussinesq numerical model and for the verification of the associated computed solution. The invariants of motions can be used as verification tools for the conservation properties of the numerical model.
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Hamdi, S., Enright, W., Ouellet, Y. et al. Exact Solutions of Extended Boussinesq Equations. Numerical Algorithms 37, 165–175 (2004). https://doi.org/10.1023/B:NUMA.0000049464.45146.88
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DOI: https://doi.org/10.1023/B:NUMA.0000049464.45146.88