TY - JOUR
T1 - On the multi-symplectic structure of Boussinesq-type systems. II
T2 - Geometric discretization
AU - Durán, Angel
AU - Dutykh, Denys
AU - Mitsotakis, Dimitrios
N1 - Funding Information:
AD was supported by Junta de Castilla y Leon and Fondos FEDER under the Grant VA041P17 . DM’s work was supported by the Marsden Fund administered by the Royal Society of New Zealand with contract number VUW1418 . AD and DM would like to acknowledge the support from the University Savoie Mont Blanc and the hospitality of LAMA UMR #5127 during their respective visits in 2019.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/10
Y1 - 2019/10
N2 - In this paper we consider the numerical approximation of systems of BOUSSINESQ-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and HAMILTONIAN formulations, well-posedness and existence of solitary-wave solutions)were previously analysed by the authors in Part I. As a second part of the study, considered here is the construction of geometric schemes for the numerical integration. By using the method of lines, the geometric properties, based on the multi-symplectic and HAMILTONIAN structures, of different strategies for the spatial and time discretizations are discussed and illustrated.
AB - In this paper we consider the numerical approximation of systems of BOUSSINESQ-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and HAMILTONIAN formulations, well-posedness and existence of solitary-wave solutions)were previously analysed by the authors in Part I. As a second part of the study, considered here is the construction of geometric schemes for the numerical integration. By using the method of lines, the geometric properties, based on the multi-symplectic and HAMILTONIAN structures, of different strategies for the spatial and time discretizations are discussed and illustrated.
KW - Boussinesq equations
KW - Geometric numerical integration
KW - Multi-symplectic schemes
KW - Surface waves
KW - Symplectic methods
UR - http://www.scopus.com/inward/record.url?scp=85066263903&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2019.05.002
DO - 10.1016/j.physd.2019.05.002
M3 - Article
AN - SCOPUS:85066263903
SN - 0167-2789
VL - 397
SP - 1
EP - 16
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
ER -