... 724 NONLINEAR PARTIAL DIFFERENTIAL EQUATIONSSimilarly, it can be established that the following special forms ... Solutions15.8.3-1. Using symmetries of equations for constructing one-parameter solutions.Suppose a particular solution,w = g(x, y), (15.8.3.1)of a given equation is known. Let us show that any ... from Subsection 15.8.2)X3= 2t∂t+ x∂x.Invariants of X3are found for the linear first-order partial differential equation X3I = 0,or2t∂I∂t+ x∂I∂x+ 0∂I∂w= 0.The associated characteristic...