Self-similar solutions of a generalized Burgers equation with nonlinear damping |
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Authors: | Ch. Srinivasa Rao P. L. Sachdev Mythily Ramaswamy |
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Affiliation: | a Department of Mathematics and Humanities, Regional Engineering College, Warangal 506 004, India;b Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India;c TIFR Centre, Indian Institute of Science Campus, Bangalore 560 012, India |
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Abstract: | The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming certain asymptotic conditions at plus infinity or minus infinity, we find a wide variety of solutions—(positive) single hump, monotonic (bounded or unbounded) or solutions with a finite zero. The existence or non-existence of positive bounded solutions with exponential decay to zero at infinity for specific parameter ranges is proved. The analysis relies mainly on the shooting argument. |
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Keywords: | Generalized Burgers equation Self-similar solution Connection problem Shooting argument |
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