Abstract
Bifurcation analysis of tsunami waves for the modified geophysical Korteweg–de Vries equation (mGKdV) is investigated through phase plots and time series plots. Using traveling wave transformation, the mGKdV equation is converted to a dynamical system. Using phase plot analysis, existence of the solitary, periodic, superperiodic tsunami waves is obtained. The Coriolis parameter (\(\omega _0\)), nonlinear parameter (a), and velocity (v) of traveling wave have significant effects on these tsunami waves.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Lighthill J (2001) Waves in fluids, 2nd edn. Cambridge University Press, Cambridge
Geyer A, Quirchmayr R (2018) Shallow water equations for equatorial tsunami waves. Philos Trans R Soc A 376(2111):20170100. https://doi.org/10.1098/rsta.2017.0100
Constantin A, Johnson RS (2008) On the non-dimensionalisation, scaling and resulting interpretation of the classical governing equations for water waves. J Nonlinear Math Phys 15:58–73. https://doi.org/10.2991/jnmp.2008.15.s2.5
Korteweg DJ, de Vries G (1895) XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. https://doi.org/10.1080/14786449508620739
Wazwaz A-M (2017) A two-mode modified KdV equation with multiple soliton solutions. Appl Math Lett 70:1–6. https://doi.org/10.1016/j.aml.2017.02.015
van Wijmgaarden L (1972) On the motion of gas bubbles in a perfect fluid. Ann Rev Fluid Mech 4:369–373. https://doi.org/10.1007/BF00037735
Stuhlmeier R (2009) KdV theory and the Chilean tsunami of 1960. Discret Continous Dyn Syst Ser B 12:623–632. https://doi.org/10.3934/dcdsb.2009.12.623
Karunakar P, Chakraverty S (2019) Effect of Coriolis constant on geophysical Korteweg-de Vries equation. J Ocean Eng Sci 4(2):113–121. https://doi.org/10.1016/j.joes.2019.02.002
Kirby JT, Shi F, Tehranirad B, Harris JC, Grilli ST (2013) Dispersive tsunami waves in the ocean: model equations and sensitivity to dispersion and Coriolis effects. Ocean Model 62:39–55. https://doi.org/10.1016/j.ocemod.2012.11.009
Lakshmanan M, Rajasekar S (2003) Nonlinear Dynamics. Springer, Heidelberg
Saha A (2012) Bifurcation of traveling wave solutions for the generalized KP-MEW equations. Commun Nonlinear Sci Numer Simul. 17:3539. https://doi.org/10.1016/j.cnsns.2012.01.005
Saha A (2017) Bifurcation, periodic and chaotic motions of the modified equal width burgers (MEW-Burgers) equation with external periodic perturbation. Nonlinear Dyn 87:2193–2201. https://doi.org/10.1007/s11071-016-3183-5
Acknowledgements
This research work is funded by TMA Pai University Research Grant (6100/SMIT/R&D/26/2019), SMIT, SMU.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Jha, A., Tyagi, M., Anand, H., Saha, A. (2021). Bifurcation Analysis of Tsunami Waves for the Modified Geophysical Korteweg–de Vries Equation. In: Giri, D., Buyya, R., Ponnusamy, S., De, D., Adamatzky, A., Abawajy, J.H. (eds) Proceedings of the Sixth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1262. Springer, Singapore. https://doi.org/10.1007/978-981-15-8061-1_6
Download citation
DOI: https://doi.org/10.1007/978-981-15-8061-1_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-8060-4
Online ISBN: 978-981-15-8061-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)