Weak surface energy in nematic dispersions: Saturn ring defects and quadrupolar interactions

The role of surface energy in the behavior of colloidal particles in liquid crystalline phases is investigated. When the surface energy dominates, a hedgehog defect is formed and, according to an electrostatic analogy, the distortions around the particles exhibit a dipolar character. By contrast, for weaker anchoring, the configuration becomes quadrupolar as evidenced by the structure of latex clusters in lyotropic systems and the observation of defects reminiscent of Saturn rings in thermotropic systems. Received 21 June 1999     

Application of Exp-function method to the Whitham–Broer–Kaup shallow water model using symbolic computation

In this letter, the Exp-function method is applied to the Whitham–Broer–Kaup shallow water model. With the help of symbolic computation, several kinds of new solitary wave solutions are formally derived.     

Lie Algebra and Lie Super Algebra for Integrable Couplings of C-KdV Hierarchy

Based on the constructed Lie algebra and Lie super algebra, the integrable couplings and super-integrable couplings of the C-KdV hierarchy are obtained respectively. Furthermore, its super-Hamiltonian structures are presented by using super-trace identity.     

Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem

The hierarchy of integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of linearization of these equations and their conservation law in the terms of solutions of corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of linearized equation due to the Noether's theorem. The local hierarchy and three nonlocal ones of the infinitesimal symmetries and conservation laws explicitly expressed through the variables of the nonlinear equations are derived.     

Some quasi-periodic solutions to the Kadometsev-Petviashvili and modified Kadometsev-Petviashvili equations

The Kadometsev-Petviashvili (KP) and modified KP (mKP) equations are retrieved from the first two soliton equations of coupled Korteweg-de Vries (cKdV) hierarchy. Based on the nonlinearization of Lax pairs, the KP and mKP equations are ultimately reduced to integrable finite-dimensional Hamiltonian systems in view of the r-matrix theory. Finally, the resulting Hamiltonian flows are linearized in Abel-Jacobi coordinates, such that some specially explicit quasi-periodic solutions to the KP and mKP equations are synchronously given in terms of theta functions through the Jacobi inversion.     

Cross Soliton-Like Waves for the （2＋1）-Dimensional Breaking Soliton Equation

We construct a two-soliton-like solution for the （2＋1）-dimensionai breaking soliton equation. The obtained solution contains two arbitrary functions and hence can model various cross soliton-like waves including the two-solitary waves. We show the evolution of some special cross soliton-like waves diagrammatically.     

In Appreciation

Leslie Foldy’s diminutive stature and modest demeanor gave little clue to the powerful intellect responsible for several significant advances in theoretical physics.Two were particularly important. His 1945 theory of the multiple scattering of waves laid out the fundamentals that most modern theories have followed (and sometimes rediscovered), while his work with Siegfried Wouthuysen on the nonrelativistic limit of the Dirac equation opened the way to a wealth of valuable insights. In this article we recall some of the milestones along Foldy’s path through a life in physics. Some of the anecdotes we report here were related to one of the authors (PLT) just before an event in 2000 celebrating Foldy’s 80th birthday, while others were told to us over the course of the nearly forty years during which we were colleagues. Still others were uncovered during the course of WJF’s research for his book, Physics at a Research University: Case Western Reserve 1830–1990 (Cleveland: Case Western Reserve University, 2006). Other details were provided by Foldy’s widow, Roma. Philip L. Taylor is the Perkins Professor of Physics and Professor of Macromolecular Science and Engineering at Case Western Reserve University. William J. Fickinger is Professor Emeritus of Physics at Case Western Reserve University.     

Induced explode-decay dromions in the (2 + 1) dimensional nonisospectral nonlinear Schrödinger (NLS) equation

In this paper, we have identified a novel method of inducing localized solutions in the (2+1) dimensional nonisospectral nonlinear Schr?dinger (NLS) equation by utilising the freedom in the system. The new class of localized solutions includes induced dromions, lump dromions, dipole dromions etc. The amplitude of the localized solutions generated is found to explode or decay with time. We have also brought out the interaction of induced dromions.     

New positon, negaton and complexiton solutions for the Bogoyavlensky-Konoplechenko equation

New positon, negaton and complexiton solutions for the Bogoyavlensky-Konoplechenko equation are constructed by means of the Darboux transformation with constant seed solution. The new positon, negaton and complexiton solutions are analytical or singular and given out both analytically and graphically.