ABSTRACT
Any linear first-order system of two real equations in the plane https://www.w3.org/1998/Math/MathML">a11(x,y)∂u1∂x+a12∂u2∂x+b11(x,y)∂u1∂y+b12(x,y)∂u2∂y+c11(x,y)u1+c12(x,y)u2=f1(x,y)a21(x,y)∂u1∂x+a22∂u2∂x+b21(x,y)∂u1∂y+b22(x,y)∂u2∂y+c21(x,y)u1+c22(x,y)u2=f2(x,y)https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062233/9da0ee55-ab85-4900-bd1b-460e01b2ece9/content/eqn0001.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> may be put in the complex form https://www.w3.org/1998/Math/MathML">a(z)wz¯+b(z)w¯z+c(z)wzd(z)w¯z+a0(z)w+b0(z)w¯=f(z),https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062233/9da0ee55-ab85-4900-bd1b-460e01b2ece9/content/eqn1_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where all quantities are now complex valued.
