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New multiple analytic solitonary solutions and simulation of (2+1)-dimensional generalized Benjamin-Bona-Mahony-Burgers model

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Abstract

In this article, the authors analyze the dynamics of new soliton-type analytical solutions and simulate the generalized Benjamin-Bona-Mahony-Burgers (GBBMB) model. First of all, tanh-coth and exp-function methods are employed to obtain the soliton analytic solutions of 1D and 2D GBBMB models and after that, the infinite domain interval is truncated to approximate the finite domain interval. Further, an algorithm based on Galerkin finite element is developed to simulate the model. In the development of the algorithm, Banach-Alaoglu theorem is used to prove the existence and uniqueness of the weak solution in \(H_{0}^{1}(\Omega )\) Sobolev space and the error estimates of the semidiscrete scheme are discussed in the \({L^{2}(0,T;H_{0}^{1}(\Omega ))}\) and \({L^{\infty }(0,T;H_{0}^{1}(\Omega ))}\) norms using the Ritz projection. In the end, various numerical problems are examined to check the chastity and competence of the proposed algorithm and the obtained soliton solutions in Sect. 2 are validated by the developed algorithm.

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The authors used the Matlab to trace the dynamics of several solitons. There are no data taken from outside sources.

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Funding

The first author, Ankur, is extremely grateful for financial support from the University Grant Commission India, ID. No. JUNE18-416131, and the second author, Ram Jiwari, is truly thankful for financial support from the National Board of Higher Mathematics (NBHM), India, with grant No. 02011/3/2021NBHM(R.P)/R &D II/6974.

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  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Ankur & Ram Jiwari

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Correspondence to Ram Jiwari.

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Ankur, Jiwari, R. New multiple analytic solitonary solutions and simulation of (2+1)-dimensional generalized Benjamin-Bona-Mahony-Burgers model. Nonlinear Dyn 111, 13297–13325 (2023). https://doi.org/10.1007/s11071-023-08528-1

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