On a new modified equation for the (x, t) interchanged KdV equation

We have obtained a new kind of x − t interchanged modified KdV system via a different type of Miura transformation obtained by using the zero curvature formulation in conjunction with Birkhoff factorization and loop algebra decomposition. The Lax pair for this new system is also deduced. The usual x − t interchanged mkdV equation is also deduced as an intermediate step.