Abstract:
It is shown that the scale invariance of equations of hydrodynamic type leads to an algebraic construction of a series of group-invariant solutions corresponding to the generalized hodograph method. A solution of Whitham's equations for the KdV equation is obtained for certain initial conditions.
Citation:
V. R. Kudashev, S. E. Sharapov, “Generalized hodograph method from the group-theoretical point of view”, TMF, 85:2 (1990), 205–210; Theoret. and Math. Phys., 85:2 (1990), 1155–1159