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Based on the positive quadratic function method, the rich nonautonomous solutions of a generalized (2+1)-dimensional variable-coefficient breaking soliton equation with different wave structures are given. In this case, due to the influence of nonlinearity and dispersion, the characteristics, amplitude and velocity of nonautonomous wave will change with time. The breather wave and the interaction among lump wave, solitary wave and periodic wave solutions are studied. For different choices of arbitrary functions in these solutions, the corresponding dynamic properties are demonstrated.

In this article, the dynamics of modified nonlinear waves for the generalized breaking soliton (gBS) equation have been explored by using analytical and numerical approaches. Firstly, the Tanh method is used to derive the solitonic solutions of the considered equation and their graphical illustrations for different values of parameters have been discussed. By using the proposed strategy, a variety of solutions can be found. Furthermore, the Galilean transformation is used to investigate the bifurcation behavior of the model. All possible phase portraits have been drawn and examined in detail. More specifically, it is shown that under defined parametric restrictions, the model has a straightforward specific value. At each fixed point, the existence of periodic points and bifurcation analysis is also confirmed. To clarify theoretical results, detailed numerical simulations are offered. Then by introducing perturbed term, the periodic and quasi-periodic behaviors of the discussed equation for various initial values are reported. Different periodic solutions can also be found in this parameter zone. Furthermore, it is reported that discussed equation is multi-stable for different values of parameters. Finally, sensitivity analysis for different initial value problems has been elaborated.

We have employed the exp(-φ(ξ))-expansion method to derive traveling waves solutions of breaking solition (BS), Zakharov-Kuznetsov-Burgers (ZKB), Ablowitz-Kaup-Newell-Segur (AKNS) water wave, Unstable nonlinear Schrödinger (UNLS) and Dodd-Bullough-Mikhailov (DBM) equations. These models have valuable applications in mathematical physics. The results of the constructed model, along with some graphical representations provide the basic knowlegde about these models. The derived results have various applications in applied science.