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Group-Invariant Solutions and Conservation Laws of One-Dimensional Nonlinear Wave Equation
  
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KeyWord:One-dimensional nonlinear wave equation, Lie symmetry, optimal system, conservation law
Author NameAffiliation
Ben Yang School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252000, China 
Yunjia Song School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252000, China 
Yanzhi Ma School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252000, China 
Xinxue Zhang School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252000, China 
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Abstract:
      Based on classical Lie symmetry method, the one-dimensional nonlinear wave equation is investigated. By using four-dimensional subalgebras of the equation, the invariant groups and commutator table are constructed. Furthermore, optimal system of the equation is obtained, and the exact solutions can be gained by solving reduced equations. Finally, a complete derivation of the conservation law is given by using conservation multipliers.