Abstract
In this paper, the conservation laws, significant symmetries’ application, and traveling wave solutions are obtained for Burger–Fisher equation (BFE). Conservation laws have a great importance for partial and fractional differential equations and their solutions, especially in physics implementations. The conservation theorem and partial Noether approach are implemented for conservation laws for this equation, and the extended sinh-Gordon expansion method (esGEM) is presented for new solitary wave solutions. All obtained conservation laws are trivial conservation laws. The new and comprehensive solitary wave solutions of the equation by the esGEM are also obtained.
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