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

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 soli ton analytic solutions of 1D and 2D GBBMB mod-els and after that, the infinite domain interval is truncated to approximate the finite domain interval. Fur-ther, 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) (O) Sobolev space and the error esti-mates of the semidiscrete scheme are discussed in the L-2(0, T; H-0(1) (O)) and L-8(0, T; H-0(1) (O)) 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 soli -ton solutions in Sect. 2 are validated by the developed algorithm.