Abstract
This paper employed the principle of undetermined coefficients and Bernoulli sub-ODE methods to acquire the topological, non-topological, periodic wave and algebraic solutions of the coupled generalized Schrödinger–Boussinesq system (CGSBs). The concept of Lie point symmetry is applied to derive the point symmetries of the CSGE. The problem on nonlinear self-adjointness of the CSGE has not been solved in previous time. In the present paper, we solve this problem and find an explicit form of the differential substitution providing the nonlinear self-adjointness. Then we use this fact to construct a set of conserved vectors using the classical symmetries admitted by the equation and the general conservation laws (Cls) theorem presented by Ibragimov. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.
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