Research ArticlesNo Access

MULTITIME BOUSSINESQ SOLITONS

University Politehnica of Bucharest, Faculty of Applied Sciences, Department of Mathematics–Informatics I, Splaiul Independentei 313, Bucharest 060042, Romania

Search for more papers by this author

CONSTANTIN UDRIŞTE

University Politehnica of Bucharest, Faculty of Applied Sciences, Department of Mathematics–Informatics I, Splaiul Independentei 313, Bucharest 060042, Romania

Search for more papers by this author

, and

CRISTIAN GHIU

University Politehnica of Bucharest, Faculty of Applied Sciences, Department of Mathematics II, Splaiul Independentei 313, Bucharest 060042, Romania

Search for more papers by this author

https://doi.org/10.1142/S0219887812500314Cited by:2 (Source: Crossref)

Abstract

The paper is devoted to the achievements of two complementary multitime missions — to state a multitime Boussinesq PDE, as geometrical prolongation of the classical one, and to obtain its multitime soliton solutions. The advantages of geometrical ingredients capable to create this significant multitime PDE are clearly shown together with problems that were or should be overcome in the similar problems. The main goal of both missions is the investigation of multitemporal Boussinesq waves. Stressing the importance of the geometry on the multitime evolution phenomena, we add original results on multitime Boussinesq solitons and on Riccati ODEs of superior order.

Keywords:

References

S. Bryson and D. Levy, SIAM J. Sci. Comput. 25(3), 767 (2003). Web of Science, Google Scholar
J. Boussinesq, C. R. Acad. Sci. Paris 72, 755 (1871). Google Scholar
J. Boussinesq, J. de Mathématique Pures et Appliquées, Deuxième Série 17, 55 (1872). Web of Science, Google Scholar
J. F. Carinena and J. de Lucas, Superposition rules and second-order Riccati equations, preprint (2010), [math-ph], 8 Jul 2010 , arXiv:1007.1309 . Google Scholar
W. Fair and Y. L. Luke, Math. Comput. 20(96), 602 (1966). Web of Science, Google Scholar
T. Meiet al., IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 24(2), 226 (2005). Web of Science, Google Scholar
O. Narayan and J. Roychowdhury, IEEE Transactions on Circuits and Systems — I: Fund. Theory Appl. 50(7), 894 (2003). Web of Science, Google Scholar
A. F. Cheviakov and G. W. Bluman, J. Math. Phys. 51, 103521 (2010). Web of Science, Google Scholar
A. F. Cheviakov and G. W. Bluman, J. Math. Phys. 51, 103522 (2010). Web of Science, Google Scholar
L. Matei and C. Udrişte, Balkan J. Geom. Appl. 16(2), 81 (2011). Web of Science, Google Scholar
L. Matei and C. Udrişte, Multitime Rayleigh solitons, preprint (2011), [math-ph] 13 Oct 2011 , arXiv:1110.2889v1 . Google Scholar
C. Udriste, L. Matei and I. Duca, Multitime Hamilton-Jacobi theory, Proceedings of 8-th WSEAS International Conference on Applied Computational Science (ACACOS-09) (Hangzhou, China, May 20–22, 2009), pp. 509–513; Proceedings of the 9-th WSEAS International Conference on Systems Theory and Scientific Computation (ISTASC-09) (Moscow, Russia, August 20–22, 2009), pp. 129–133 . Google Scholar
C. Udrişte, I. Ţevy and V. Arsinte, J. Adv. Math. Stud. 3(2), 105 (2010). Google Scholar
A. Bejenaru and C. Udrişte, Multitime optimal control and equilibrium deformations, 6th IASME/WSEAS Int. Conf. on Continuum Mechanics (CM-11)2011 (Cambridge, UK) pp. 126–136. Google Scholar
C. Udrişte, Balkan J. Geom. Appl. 16(1), 128 (2011). Google Scholar
C. Udrişte and A. Pitea, Balkan J. Geom. Appl. 16(2), 174 (2011). Google Scholar
C. Udrişte, V. Arsinte and C. Cipu, Balkan J. Geom. Appl. 16(1), 150 (2011). Google Scholar
C. Udrişte and A. Bejenaru, Balkan J. Geom. Appl. 16(2), 138 (2011). Google Scholar
C. Udrişte and I. Ţevy, Balkan J. Geom. Appl. 16(1), 155 (2011). Google Scholar
C. Udrişte, Multitime optimal control for quantum systems, Proceedings of Third Int. Conf. on Lie-Admissible Treatments of Irreversible Processes (ICLATIP-3) (Kathmandu University, Dhulikhel, Nepal, 2011) pp. 203–218. Google Scholar
S. Weinstein, Multiple time dimensions, preprint (2008), [physics. gen-ph] 19 Dec 2008 , arXiv:0812.3869v1 . Google Scholar