We present a review of the normal form theory for weakly dispersive nonlinear wave equations where the leading order phenomena can be described by the KdV equation. This is an infinite dimensional extension of the well-known Poincaré-Dulac normal form theory for ordinary differential equations. We also provide a detailed analysis of the interaction problem of solitary waves as an important appl...

Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry, in which at least two trees are planted for each one used for paper production. Contents Foreword xi Editor's preface to the Manchester Physics Series xiii Author's preface xv 1 PLANCK'S CONSTANT IN ACTION 1.1 Photons 1 1.2 De B...

This paper describes the effects of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluids in an asymmetric channel. The two dimensional equation of couple stress fluid are simplified by making the assumptions of long wave length and low Reynolds number. The exact solutions of reduced momentum equation and magnetic force function have been computed in wave...

In this paper, we consider the derivation of the Kadomtsev-Petviashvili (KP) equation for cold ion-acoustic wave in the long wavelength limit of the two-dimensional quantum Euler-Poisson system, under different scalings for varying directions in the Gardner-Morikawa transform. It is shown that the types of the KP equation depend on the scaled quantum parameter H > 0. The QKP-I is derived for H ...

In this paper, by means of the general projective Riccati equation method (PREM), the variable separation solutions of the (2+1)-dimensional modified dispersive water-wave system are obtained. By further studying, we find that these variable separation solutions, which seem independent, actually depend on each other. Based on the special variable separation solution and choosing suitable functi...

this paper describes the effects of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluids in an asymmetric channel. the two dimensional equation of couple stress fluid are simplified by making the assumptions of long wave length and low reynolds number. the exact solutions of reduced momentum equation and magnetic force function have been computed in wave fra...

New manifestly gauge-invariant forms of two-dimensional generalized dispersive long wave and NizhnikVeselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous two-dimensional generalization of dispersive long wave system of equations, Nizhnik-Veselov-Novikov and modified Nizhnik-Veselov-Novikov equations and other known an...