Abstract
An attempt has been made to obtain exact analytical travelling wave solution of Korteweg-de Vries-Burger's (KdVB) equation by the so-called tanh-method. This equation can be derived for dust ion acoustic shocks by using reduction perturbation method. It is found that an exact solution of the KdVB equation is obtained by tanh-method, provided the parameters involved satisfy a constraint relation. However a special exact analytical solution can be obtained where no such restriction is necessary. This solution has the structure of a shock wave. Numerical solution is also obtained for travelling wave with or without the assumption of the constraint relation. We have also found a singular solution in terms of cosech and coth functions.
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Sahu, B., Roychoudhury, R. Travelling Wave Solution of Korteweg-de Vries-Burger's Equation. Czechoslovak Journal of Physics 53, 517–527 (2003). https://doi.org/10.1023/A:1024657626565
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DOI: https://doi.org/10.1023/A:1024657626565