New conservation laws obtained directly from symmetry action on a known conservation law |
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Authors: | George Bluman Temuerchaolu Stephen C Anco |
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Institution: | a Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2 b Department of Mathematics, Brock University, St. Catharines, ON, Canada L2S 3A1 |
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Abstract: | Two formulas are introduced to directly obtain new conservation laws for any system of partial differential equations from a known conservation law and admitted symmetries. The first formula maps any conservation law of a given system to the corresponding conservation law of the system obtained through a contact transformation. When the contact transformation is a symmetry of the given system, then the corresponding conservation law is a conservation law of the given system. The second formula checks a priori whether or not the action of a symmetry (continuous or discrete) on a conservation law can yield one or more new conservation laws of the given system. Several examples are considered, including the use of a discrete symmetry to obtain a new conservation law and the use of a continuous symmetry to generate two new conservation laws. |
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Keywords: | Conservation laws Symmetry Nonlinear telegraph equations Cylindrical KdV equation |
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