Travelling Wave Solution of Korteweg-de Vries-Burger's Equation |
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Authors: | Biswajit Sahu Rajkumar Roychoudhury |
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Affiliation: | (1) Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India |
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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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Keywords: | Korteweg-de Vries-Burger's equation tanh method dust ion acoustic waves travelling wave solution hyperbolic function method |
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