Strain solitons in solids and how to construct them (Q2734573)

The concept of soliton can be regarded as one of the major discoveries in mathematical sciences in the second half of the twentieth century. The last four decades have produced major advances in mathematical, physical, and computational aspects of solitons. Studies are continually being added to soliton dynamics in fluids and solids. This book by Professor Alexander Samsonov is the first serious attempt to present the general theory of wave propagation in nonlinear elastic solids based on the principles of nonlinear elasticity. The book describes recent development of the theory, generation and propagation of strain solitons in solids, and presents some numerical results. The book has six chapters, conclusive remarks and tentative applications, bibliography, and an appendix. The author is known for his own contributions to nonlinear waves and solitons in elastic solids, and his research interests have naturally influenced the choice of the topics in this book.NEWLINENEWLINENEWLINEThe opening chapter deals with nonlinear waves in elastic solids. It includes basic ideas and definitions of linear and nonlinear waves, deformation, stresses and strains, physical and geometrical sources of nonlinearity, compressibility, dispersion and dissipation in wav- guides. Chapter 2 gives a mathematical description of the general deformation wave problem. It contains a short discussion on action functional and Lagrange formalism, coupled equations of long waves, one-dimensional quasilinear hyperbolic equations, derivation of the doubly dispersive wave equations, equations for wave in non-uniform highly nonlinear wave-guide, and equations for waves in a wave-guide embedded in an extremal medium. Chapter 3 is devoted to direct methods and formal solutions of nonlinear hyperbolic and evolution equations, dissipative nonlinear equations, and nonlinear reaction-diffusion equations. Special attention is given to travelling wave solutions, discontinuous solutions, periodic and solitary wave solutions, autosoliton solutions and periodic bounded solutions. A brief discussion is made on conservation laws, Hamiltonian structure and general reduction theorem. Nonlinear strain waves in elastic wave-guides are discussed in chapter 4. This chapter deals with special features of longitudinal waves in a rod, and with solitons in inhomogeneous elastic rods. Particular attention is given to experimental observations of soliton propagation in a nonuniform rod. Chapter 5 examines nonlinear waves in complex wave-guides. This includes longitudinal nonlinear waves in an elastic plate, longitudinal waves in rods embedded in a surrounding medium, and nonlinear waves in surrounding medium and nonlinear waves in a layered elastic half-space. Some emphasis is given to physical experiments concerning waves in a layered medium. The final chapter describes numerical simulation of solitary waves in elastic solids in various configurations. This is followed by conclusive remarks and tentative applications.NEWLINENEWLINENEWLINEThis book is written to stimulate further study and research in this growing and important field. This is not a typical graduate-level textbook as there are no exercises; however, it could be used in graduate-level seminar courses. This book is well written, and it does not contain any wrong information or errors. In the reviewer's opinion, this is an excellent addition to the literature on solitons in elastic solids.