On multiperiodic and multisoliton solutions to evolution equations with applications
Department of Mathematics, Faculty of Science, Cairo University, Cairo, Egypt
Accepted: 3 December 2010
Published online: 11 February 2011
The existence of multiperiodic and multisoliton solutions for parabolic one-dimensional scalar and vector equations is studied. It is shown that these solutions exist for a scalar equation if it is completely integrable and linearizable, while they exist for vector equations when they are completely integrable. The geometric structure of the solutions is similar to that of multidimensional equations. As applications, vector equations for Burger’s, KdV, KdV-Burgers and Kuramoto-Sivashinsky equations are considered.
© Società Italiana di Fisica and Springer, 2011