Multi-Soliton Solutions to the Generalized Boussinesq Equation of Tenth Order

Document Type : Research Paper


1 PG Department of Mathematics, PG Studies and Research Centre, St. Philomena's College, Mysuru-570 015, India.

2 Department of Studies in Mathematics,University of Mysore, Manasagangothri, Mysuru-570 006, India.


In the recent literature, many researchers are interested to apply standard computational methods for exact or numerical solutions of many classical nonlinear partial differential equations. Some leading methods are based on Lie group analysis, Painleve Analysis, G0/G expansion techniques, homotopy perturbation methods, and so on. The equations include complicated Navier-Stokes equation, Schrodinger equation, KdV-like equations, and so on. As a result, the glory of nonlinear dynamics can be witnessed through its applications in many fields namely: ocean engineering, plasma physics, optical communications, fluid dynamics, and much more. One of the significant observations is that whatever may be the order of nonlinear PDE, as far as the soliton and multisolitons of KdV like equation or Boussinesq equation are concerned Hirota’s method and tanh − coth method play a crucial role. The main result of the paper demonstrates that the above novel theme works well with the generalized Boussinesq equation of 10th order. In this paper, the Boussinesq equation of order ten is derived and its multi-soliton solutions are deduced by the Hirota’s method. The one soliton solution is reconfirmed using the tanh method. 


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