Abstract
In this work, while applying a new and novel (G'/G)-expansion version technique, we identify four families of the traveling wave solutions to the (1 + 1)-dimensional compound KdVB equation. The exact solutions are derived, in terms of hyperbolic, trigonometric and rational functions, involving various parameters. When the parameters are tuned to special values, both solitary, and periodic wave models are distinguished. State of the art symbolic algebra graphical representations and dynamical interpretations of the obtained solutions physics are provided and discussed. This in turn ends up revealing salient solutions features and demonstrating the used method efficiency.
Highlights
Nonlinear Evolution Equations (NLEEs) are encountered in various fields of engineering, and many theoretical and applied sciences physics, such as applied mathematics, chemistry, biology and many applications
The aim of this article is to demonstrate the efficiency of the novel (G′/G)-expansion method to exhibit exact solutions for NLEEs in mathematical physics via the (1 + 1)-dimensional compound KdVB equation [36]
On the other hand, introducing nonlinearity without dispersion prevents the formation of solitary waves, because the pulse energy is frequently pumped into higher frequency modes
Summary
Nonlinear Evolution Equations (NLEEs) are encountered in various fields of engineering, and many theoretical and applied sciences physics, such as applied mathematics, chemistry, biology and many applications. Exact analytical solutions of NLEEs have come to play a significant role in understanding of qualitative nature of. Graphical representations of solutions of the NLEEs equations permit the unscrambling of mechanisms pertaining to compound nonlinear phenomena. This includes for instance spatial localization of transfer processes, multiplicity or non-appearance steady states under different conditions, and existence of peaking regimes. Even special exact solutions data that may seem not to have a clear physical meaning, can often be used as test problems to verify processes reliability, and help estimate errors of various numerical, asymptotic, and approximate analytical methods
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