Abstract
The known model of nonlinear dispersive waves, which was proposed by Boussinesq in the second half of the nineteenth century, is considered. Solutions of the Boussinesq equation, which are expressed via elementary functions and describe wave packets, their interaction between each other and with solitons, and some other structures are obtained. To construct these solutions, Hirota's bilinear representation and differential relations specified by ordinary differential equations with constant coefficients are used.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Bhatnagar,Nonlinear Waves in One-Dimensional Dispersive Systems, Clarendon Press, Oxford (1979).
G. B. Whitham,Linear and Nonlinear Waves, John Wiley and Sons, New York (1974).
R. Hirota, “ExactN-soliton solution of the wave equation of long waves in shallow water and in nonlinear lattices”,J. Math. Phys.,14, 810–814 (1973).
M. Ablowitz and H. Segur,Solitons and Inverse Scattering Transform, SIAM, Philadelphia (1981).
J. Lighthill,Waves in Fluids, Cambridge Univ. Press. Cambridge (1978).
G. L. Lamb, Jr.,Elements of Soliton Theory, John Wiley and Sons, New York (1980).
Additional information
Computing Center, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 74–78, May–June, 1998.
Rights and permissions
About this article
Cite this article
Kaptsov, O.V. Construction of exact solutions of the Boussinesq equation. J Appl Mech Tech Phys 39, 389–392 (1998). https://doi.org/10.1007/BF02468120
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02468120