Symmetry reductions, exact solutions, and conservation laws of a modified Hunter-Saxton equation
Summary: We study a modified Hunter-Saxton equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the underlying equation are derived. We utilize the Lie algebra admitted by the equation to obtain the optimal system of one-dimensional subalgebras of the Lie algebra of the equation. These subalgebras are then used to reduce the underlying equation to nonlinear third-order ordinary differential equations. Exact traveling wave group-invariant solutions for the equation are constructed by integrating the reduced ordinary differential equations. Moreover, using the variational method, we construct infinite number of nonlocal conservation laws by the transformation of the dependent variable of the underlying equation.
exact group-invariant traveling wave solutions
optimal system of one-dimensional subalgebras
scientific article; zbMATH DE number 6306524
scientific article