Similarity analysis of modified shallow water equations and evolution of weak waves |
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Authors: | T Raja Sekhar VD Sharma |
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Institution: | a Department of Mathematics, National Institute of Technology Rourkela, Rourkela-8, India b Department of Mathematics, Indian Institute of Technology Bombay, Mumbai-76, India |
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Abstract: | In this paper, we obtain exact solutions to the nonlinear system of partial differential equations (PDEs), describing the one dimensional modified shallow water equations, using invariance group properties of the governing system. Lie group of point symmetries with commuting infinitesimal operators, are presented. The symmetry generators are used for constructing similarity variables which lead the governing system of PDEs to system of ordinary differential equations (ODEs); in some cases, it is possible to solve these equations exactly. A particular solution to the governing system, which exhibits space-time dependence, is used to study the evolutionary behavior of weak discontinuities. |
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Keywords: | Modified shallow water equations Group theoretic method Exact solution Weak discontinuity |
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