The Laplace transform method (LTM) is introduced to solve Burgers’ equation. Because of the nonlinear term in Burgers’ equation, one cannot directly apply the LTM. Increment linearization technique is introduced to deal with the situation. This is a key idea in this paper. The increment linearization technique is the following: In time level t , we divide the solution u(x, t) into two parts: u(...

In this work, a new approach of the Kekre transform in the integral form is introduced. A theory of operation matrix is developed by numerical computation and by partitioning of the matrices in four submatrices which is proved as the same. An operational matrices of integration based on Kekre transform are applied to the dynamic systems with distributed parameters to analyse their applications....

There exist certain nonlinear evolution PDEs which can be mapped to linear evolution PDEs. The prototypical such linearizable PDE is the so-called Burger's equation u t − u xx = 2uu x , (1.1) which can be written in the conservation form ∂ t u = ∂ x (u x + u 2). Employing the so-called Cole-Hopf transformation u = q x q (1.2) and using the identity ∂ t q x q = ∂ t ∂ x ln q = ∂ x ∂ t ln q = ∂ x ...

The possibilities to run with a linear collider at the Z-pole with high luminosity are examined. Apart from the implications on machine and detector the interest for electroweak and B-physics is discussed. Plenary talk at the International Workshop on Linear Colliders, Fermilab 24 28 October 2000